Ch06-varselect-lab.ipynb

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    "\n",
    "# Linear Models and Regularization Methods\n",
    "\n",
    "<a target=\"_blank\" href=\"https://colab.research.google.com/github/intro-stat-learning/ISLP_labs/blob/v2.2/Ch06-varselect-lab.ipynb\">\n",
    "<img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/>\n",
    "</a>\n",
    "\n",
    "[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/intro-stat-learning/ISLP_labs/v2.2?labpath=Ch06-varselect-lab.ipynb)"
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   "source": [
    "In this lab we implement many of the techniques discussed in this chapter.\n",
    "We import some of our libraries at this top\n",
    "level. "
   ]
  },
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   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from matplotlib.pyplot import subplots\n",
    "from statsmodels.api import OLS\n",
    "import sklearn.model_selection as skm\n",
    "import sklearn.linear_model as skl\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from ISLP import load_data\n",
    "from ISLP.models import ModelSpec as MS\n",
    "from functools import partial\n"
   ]
  },
  {
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   "source": [
    "We again collect the new imports\n",
    "needed for this lab. Readers will also have to have installed `l0bnb` using `pip install l0bnb`."
   ]
  },
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   "source": [
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.cross_decomposition import PLSRegression\n",
    "from ISLP.models import \\\n",
    "     (Stepwise,\n",
    "      sklearn_selected,\n",
    "      sklearn_selection_path)\n",
    "from l0bnb import fit_path\n"
   ]
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   "source": [
    "## Subset Selection Methods\n",
    "Here we implement methods that reduce the number of parameters in a\n",
    "model by restricting the model to a subset of the input variables.\n",
    "\n",
    "### Forward Selection\n",
    " \n",
    "We will  apply the forward-selection approach to the  `Hitters` \n",
    "data.  We wish to predict a baseball player’s `Salary` on the\n",
    "basis of various statistics associated with performance in the\n",
    "previous year.\n",
    "\n",
    "First of all, we note that the `Salary` variable is missing for\n",
    "some of the players.  The `np.isnan()`  function can be used to\n",
    "identify the missing observations. It returns an array\n",
    "of the same shape as the input vector, with a `True` for any elements that\n",
    "are missing, and a `False` for non-missing elements.  The\n",
    "`sum()`  method can then be used to count all of the\n",
    "missing elements."
   ]
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   "source": [
    "Hitters = load_data('Hitters')\n",
    "np.isnan(Hitters['Salary']).sum()\n"
   ]
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   "source": [
    " We see that `Salary` is missing for 59 players. The\n",
    "`dropna()`  method of data frames removes all of the rows that have missing\n",
    "values in any variable (by default --- see  `Hitters.dropna?`)."
   ]
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   "source": [
    "Hitters = Hitters.dropna();\n",
    "Hitters.shape\n"
   ]
  },
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   "source": [
    "We first choose the best model using forward selection based on $C_p$ (\\ref{Ch6:eq:cp}). This score\n",
    "is not built in as a metric to `sklearn`. We therefore define a function to compute it ourselves, and use\n",
    "it as a scorer. By default, `sklearn` tries to maximize a score, hence\n",
    "  our scoring function  computes the negative $C_p$ statistic."
   ]
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   "source": [
    "def nCp(sigma2, estimator, X, Y):\n",
    "    \"Negative Cp statistic\"\n",
    "    n, p = X.shape\n",
    "    Yhat = estimator.predict(X)\n",
    "    RSS = np.sum((Y - Yhat)**2)\n",
    "    return -(RSS + 2 * p * sigma2) / n \n"
   ]
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   "source": [
    "We need to estimate the residual variance $\\sigma^2$, which is the first argument in our scoring function above.\n",
    "We will fit the biggest model, using all the variables, and estimate $\\sigma^2$ based on its MSE."
   ]
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   "source": [
    "design = MS(Hitters.columns.drop('Salary')).fit(Hitters)\n",
    "Y = np.array(Hitters['Salary'])\n",
    "X = design.transform(Hitters)\n",
    "sigma2 = OLS(Y,X).fit().scale\n"
   ]
  },
  {
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   "id": "bc283589",
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   "source": [
    "The function `sklearn_selected()` expects a scorer with just three arguments --- the last three in the definition of `nCp()` above. We use the function `partial()` first seen in Section~\\ref{Ch5-resample-lab:the-bootstrap} to freeze the first argument with our estimate of $\\sigma^2$."
   ]
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   "source": [
    "neg_Cp = partial(nCp, sigma2)\n"
   ]
  },
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   "source": [
    "We can now use `neg_Cp()` as a scorer for model selection.\n"
   ]
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   "source": [
    "Along with a score we need to specify the search strategy. This is done through the object\n",
    "`Stepwise()`  in the `ISLP.models` package. The method `Stepwise.first_peak()`\n",
    "runs forward stepwise until any further additions to the model do not result\n",
    "in an improvement in the evaluation score. Similarly, the method `Stepwise.fixed_steps()`\n",
    "runs a fixed number of steps of stepwise search."
   ]
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   "source": [
    "strategy = Stepwise.first_peak(design,\n",
    "                               direction='forward',\n",
    "                               max_terms=len(design.terms))\n"
   ]
  },
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    "We now fit a linear regression model with `Salary` as outcome using forward\n",
    "selection. To do so, we use the function `sklearn_selected()`  from the `ISLP.models` package. This takes\n",
    "a model from `statsmodels` along with a search strategy and selects a model with its\n",
    "`fit` method. Without specifying a `scoring` argument, the score defaults to MSE, and so all 19 variables will be\n",
    "selected."
   ]
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     "data": {
      "text/plain": [
       "('Assists',\n",
       " 'AtBat',\n",
       " 'CAtBat',\n",
       " 'CHits',\n",
       " 'CHmRun',\n",
       " 'CRBI',\n",
       " 'CRuns',\n",
       " 'CWalks',\n",
       " 'Division',\n",
       " 'Errors',\n",
       " 'Hits',\n",
       " 'HmRun',\n",
       " 'League',\n",
       " 'NewLeague',\n",
       " 'PutOuts',\n",
       " 'RBI',\n",
       " 'Runs',\n",
       " 'Walks',\n",
       " 'Years')"
      ]
     },
     "execution_count": 9,
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     "output_type": "execute_result"
    }
   ],
   "source": [
    "hitters_MSE = sklearn_selected(OLS,\n",
    "                               strategy)\n",
    "hitters_MSE.fit(Hitters, Y)\n",
    "hitters_MSE.selected_state_\n"
   ]
  },
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   "source": [
    "Using `neg_Cp` results in a smaller model, as expected, with just 10 variables selected."
   ]
  },
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     "data": {
      "text/plain": [
       "('Assists',\n",
       " 'AtBat',\n",
       " 'CAtBat',\n",
       " 'CRBI',\n",
       " 'CRuns',\n",
       " 'CWalks',\n",
       " 'Division',\n",
       " 'Hits',\n",
       " 'PutOuts',\n",
       " 'Walks')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hitters_Cp = sklearn_selected(OLS,\n",
    "                               strategy,\n",
    "                               scoring=neg_Cp)\n",
    "hitters_Cp.fit(Hitters, Y)\n",
    "hitters_Cp.selected_state_\n"
   ]
  },
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    "### Choosing Among Models Using the Validation Set Approach and Cross-Validation\n",
    " \n",
    "As an  alternative to using $C_p$, we might try cross-validation to select a model in forward selection. For this, we need a\n",
    "method that stores the full path of models found in forward selection, and allows predictions for each of these. This can be done with the `sklearn_selection_path()` \n",
    "estimator from `ISLP.models`. The function `cross_val_predict()` from `ISLP.models`\n",
    "computes the cross-validated predictions for each of the models\n",
    "along the path, which we can use to evaluate the cross-validated MSE\n",
    "along the path."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6769115d",
   "metadata": {},
   "source": [
    "Here we define a strategy that fits the full forward selection path.\n",
    "While there are various parameter choices for `sklearn_selection_path()`,\n",
    "we use the defaults here, which selects the model at each step based on the biggest reduction  in RSS."
   ]
  },
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    "strategy = Stepwise.fixed_steps(design,\n",
    "                                len(design.terms),\n",
    "                                direction='forward')\n",
    "full_path = sklearn_selection_path(OLS, strategy)\n"
   ]
  },
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   "source": [
    "We now fit the full forward-selection path on the `Hitters` data and compute the fitted values."
   ]
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   "source": [
    "full_path.fit(Hitters, Y)\n",
    "Yhat_in = full_path.predict(Hitters)\n",
    "Yhat_in.shape\n"
   ]
  },
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    "This gives us an array of fitted values --- 20 steps in all, including the fitted mean for the null model --- which we can use to evaluate\n",
    "in-sample MSE. As expected, the in-sample MSE improves each step we take,\n",
    "indicating we must use either the validation or cross-validation\n",
    "approach to select the number of steps. We fix the y-axis to range from\n",
    "50,000 to 250,000 to compare to the cross-validation and validation\n",
    "set MSE below, as well as other methods such as ridge regression, lasso and\n",
    "principal components regression."
   ]
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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mse_fig, ax = subplots(figsize=(8,8))\n",
    "insample_mse = ((Yhat_in - Y[:,None])**2).mean(0)\n",
    "n_steps = insample_mse.shape[0]\n",
    "ax.plot(np.arange(n_steps),\n",
    "        insample_mse,\n",
    "        'k', # color black\n",
    "        label='In-sample')\n",
    "ax.set_ylabel('MSE',\n",
    "              fontsize=20)\n",
    "ax.set_xlabel('# steps of forward stepwise',\n",
    "              fontsize=20)\n",
    "ax.set_xticks(np.arange(n_steps)[::2])\n",
    "ax.legend()\n",
    "ax.set_ylim([50000,250000]);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f7508e0",
   "metadata": {},
   "source": [
    "Notice the expression `None` in `Y[:,None]` above.\n",
    "This adds an axis (dimension) to the one-dimensional array `Y`,\n",
    "which allows it to be recycled when subtracted from the two-dimensional `Yhat_in`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6c9531a",
   "metadata": {},
   "source": [
    "We are now ready to use cross-validation to estimate test error along\n",
    "the model path. We must use *only the training observations* to perform all aspects of model-fitting --- including\n",
    "variable selection.  Therefore, the determination of which model of a\n",
    "given size is best must be made using \\emph{only the training\n",
    "  observations} in each training fold. This point is subtle but important.  If the full data\n",
    "set is used to select the best subset at each step, then the validation\n",
    "set errors and cross-validation errors that we obtain will not be\n",
    "accurate estimates of the test error.\n",
    "\n",
    "We now compute the cross-validated predicted values using 5-fold cross-validation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "a1654ad8",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:23.097519Z",
     "iopub.status.busy": "2024-06-04T23:19:23.097271Z",
     "iopub.status.idle": "2024-06-04T23:19:25.139415Z",
     "shell.execute_reply": "2024-06-04T23:19:25.139180Z"
    },
    "lines_to_next_cell": 0
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(263, 20)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K = 5\n",
    "kfold = skm.KFold(K,\n",
    "                  random_state=0,\n",
    "                  shuffle=True)\n",
    "Yhat_cv = skm.cross_val_predict(full_path,\n",
    "                                Hitters,\n",
    "                                Y,\n",
    "                                cv=kfold)\n",
    "Yhat_cv.shape\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98dfabdc",
   "metadata": {},
   "source": [
    "`skm.cross_val_predict()`\n",
    "The prediction matrix `Yhat_cv` is the same shape as `Yhat_in`; the difference is that the predictions in each row, corresponding to a particular sample index, were made from models fit on a training fold that did not include that row.\n",
    "\n",
    "At each model along the path, we compute the MSE in each of the cross-validation folds.\n",
    "These we will average to get the  mean MSE, and can also use the individual values to compute a crude estimate of the standard error of the mean. {The estimate is crude because the five error estimates  are based on overlapping training sets, and hence are not independent.}\n",
    "Hence we must know the test indices for each cross-validation\n",
    "split. This can be found by using the `split()` method of `kfold`. Because\n",
    "we  fixed the random state above, whenever we split any array with the same\n",
    "number of rows as $Y$ we recover the same training and test indices, though we simply\n",
    "ignore the training indices below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "ce919bd3",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:25.140773Z",
     "iopub.status.busy": "2024-06-04T23:19:25.140698Z",
     "iopub.status.idle": "2024-06-04T23:19:25.143330Z",
     "shell.execute_reply": "2024-06-04T23:19:25.143113Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20, 5)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cv_mse = []\n",
    "for train_idx, test_idx in kfold.split(Y):\n",
    "    errors = (Yhat_cv[test_idx] - Y[test_idx,None])**2\n",
    "    cv_mse.append(errors.mean(0)) # column means\n",
    "cv_mse = np.array(cv_mse).T\n",
    "cv_mse.shape\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a27004be",
   "metadata": {},
   "source": [
    "We now add the cross-validation error estimates to our MSE plot.\n",
    "We include the mean error across the five folds, and the estimate of the standard error of the mean. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "26520d22",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:25.144503Z",
     "iopub.status.busy": "2024-06-04T23:19:25.144435Z",
     "iopub.status.idle": "2024-06-04T23:19:25.201431Z",
     "shell.execute_reply": "2024-06-04T23:19:25.201214Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ax.errorbar(np.arange(n_steps), \n",
    "            cv_mse.mean(1),\n",
    "            cv_mse.std(1) / np.sqrt(K),\n",
    "            label='Cross-validated',\n",
    "            c='r') # color red\n",
    "ax.set_ylim([50000,250000])\n",
    "ax.legend()\n",
    "mse_fig\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9881566e",
   "metadata": {},
   "source": [
    "To repeat the above using the validation set approach, we simply change our\n",
    "`cv` argument to a validation set: one random split of the data into a test and training. We choose a test size\n",
    "of 20%, similar to the size of each test set in 5-fold cross-validation.`skm.ShuffleSplit()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "f19c9091",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:25.202701Z",
     "iopub.status.busy": "2024-06-04T23:19:25.202634Z",
     "iopub.status.idle": "2024-06-04T23:19:25.603532Z",
     "shell.execute_reply": "2024-06-04T23:19:25.603301Z"
    },
    "lines_to_next_cell": 0
   },
   "outputs": [],
   "source": [
    "validation = skm.ShuffleSplit(n_splits=1, \n",
    "                              test_size=0.2,\n",
    "                              random_state=0)\n",
    "for train_idx, test_idx in validation.split(Y):\n",
    "    full_path.fit(Hitters.iloc[train_idx],\n",
    "                  Y[train_idx])\n",
    "    Yhat_val = full_path.predict(Hitters.iloc[test_idx])\n",
    "    errors = (Yhat_val - Y[test_idx,None])**2\n",
    "    validation_mse = errors.mean(0)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7421fc11",
   "metadata": {},
   "source": [
    " As for the in-sample MSE case, the validation set approach does not provide standard errors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "1fca6b08",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:25.604861Z",
     "iopub.status.busy": "2024-06-04T23:19:25.604789Z",
     "iopub.status.idle": "2024-06-04T23:19:25.664722Z",
     "shell.execute_reply": "2024-06-04T23:19:25.664495Z"
    },
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ax.plot(np.arange(n_steps), \n",
    "        validation_mse,\n",
    "        'b--', # color blue, broken line\n",
    "        label='Validation')\n",
    "ax.set_xticks(np.arange(n_steps)[::2])\n",
    "ax.set_ylim([50000,250000])\n",
    "ax.legend()\n",
    "mse_fig\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4df366a",
   "metadata": {},
   "source": [
    "### Best Subset Selection\n",
    "Forward stepwise is a *greedy* selection procedure; at each step it augments the current set by including one additional variable.  We now apply best subset selection  to the  `Hitters` \n",
    "data, which for every subset size, searches for the best set of predictors.  \n",
    "\n",
    "We will use a package called `l0bnb` to perform\n",
    "best subset selection.\n",
    "Instead of constraining the subset to be a given size,\n",
    "this package produces a path of solutions using the subset size as a\n",
    "penalty rather than a constraint. Although the distinction is subtle, the difference comes when we cross-validate. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "6e9dd7d4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:25.665992Z",
     "iopub.status.busy": "2024-06-04T23:19:25.665901Z",
     "iopub.status.idle": "2024-06-04T23:19:25.679390Z",
     "shell.execute_reply": "2024-06-04T23:19:25.679171Z"
    },
    "lines_to_next_cell": 0
   },
   "outputs": [],
   "source": [
    "D = design.fit_transform(Hitters)\n",
    "D = D.drop('intercept', axis=1)\n",
    "X = np.asarray(D)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b87bd74",
   "metadata": {},
   "source": [
    "Here we excluded the first column corresponding to the intercept, as\n",
    "`l0bnb` will fit the intercept separately. We can find a path using the `fit_path()` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "caed84ae",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:25.680677Z",
     "iopub.status.busy": "2024-06-04T23:19:25.680609Z",
     "iopub.status.idle": "2024-06-04T23:19:27.246130Z",
     "shell.execute_reply": "2024-06-04T23:19:27.245877Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Preprocessing Data.\n",
      "BnB Started.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 1. Number of non-zeros:  1\n",
      "Iteration: 2. Number of non-zeros:  2\n",
      "Iteration: 3. Number of non-zeros:  2\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 4. Number of non-zeros:  2\n",
      "Iteration: 5. Number of non-zeros:  3\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 6. Number of non-zeros:  3\n",
      "Iteration: 7. Number of non-zeros:  4\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 8. Number of non-zeros:  9\n",
      "Iteration: 9. Number of non-zeros:  9\n",
      "Iteration: 10. Number of non-zeros:  9\n",
      "Iteration: 11. Number of non-zeros:  9\n",
      "Iteration: 12. Number of non-zeros:  9\n",
      "Iteration: 13. Number of non-zeros:  9\n",
      "Iteration: 14. Number of non-zeros:  9\n",
      "Iteration: 15. Number of non-zeros:  9\n",
      "Iteration: 16. Number of non-zeros:  9\n",
      "Iteration: 17. Number of non-zeros:  9\n",
      "Iteration: 18. Number of non-zeros:  17\n",
      "Iteration: 19. Number of non-zeros:  19\n"
     ]
    }
   ],
   "source": [
    "path = fit_path(X, \n",
    "                Y,\n",
    "                max_nonzeros=X.shape[1])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4e9ca6a",
   "metadata": {},
   "source": [
    "The function `fit_path()` returns a list whose values include the fitted coefficients as `B`, an intercept as `B0`, as well as a few other attributes related to the particular path algorithm used. Such details are beyond the scope of this book."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "f2fc2ef8",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:27.247604Z",
     "iopub.status.busy": "2024-06-04T23:19:27.247525Z",
     "iopub.status.idle": "2024-06-04T23:19:27.249696Z",
     "shell.execute_reply": "2024-06-04T23:19:27.249497Z"
    },
    "lines_to_next_cell": 0
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'B': array([0.        , 3.25484367, 0.        , 0.        , 0.        ,\n",
       "        0.        , 0.        , 0.        , 0.        , 0.        ,\n",
       "        0.        , 0.67775265, 0.        , 0.        , 0.        ,\n",
       "        0.        , 0.        , 0.        , 0.        ]),\n",
       " 'B0': -38.98216739555551,\n",
       " 'lambda_0': 0.011416248027450178,\n",
       " 'M': 0.5829861733382012,\n",
       " 'Time_exceeded': False}"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path[3]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4a96126",
   "metadata": {},
   "source": [
    "In the example above, we see that at the fourth step in the path, we have two nonzero coefficients in `'B'`, corresponding to the value $0.114$ for the penalty parameter `lambda_0`.\n",
    "We could make predictions using this sequence of fits on a validation set as a function of `lambda_0`, or with more work using cross-validation.\n",
    "\n",
    "## Ridge Regression and the Lasso\n",
    "We will use the `sklearn.linear_model` package (for which\n",
    "we use `skl` as shorthand below)\n",
    "to fit ridge and  lasso regularized linear models on the `Hitters` data.\n",
    "We start with the model matrix `X` (without an intercept) that we computed in the previous section on best subset regression.\n",
    "\n",
    "### Ridge Regression\n",
    "We will use the function `skl.ElasticNet()` to fit both  ridge and the lasso.\n",
    "To fit a *path* of ridge regressions models, we use\n",
    "`skl.ElasticNet.path()`, which can fit both ridge and lasso, as well as a hybrid mixture;  ridge regression\n",
    "corresponds to `l1_ratio=0`.\n",
    "It is good practice to standardize the columns of `X` in these applications, if the variables are measured in different units. Since `skl.ElasticNet()` does no normalization, we have to take care of that ourselves.\n",
    "Since we\n",
    "standardize first, in order to find coefficient\n",
    "estimates on the original scale, we must *unstandardize*\n",
    "the coefficient estimates. The parameter\n",
    "$\\lambda$ in (\\ref{Ch6:ridge}) and (\\ref{Ch6:LASSO}) is called `alphas` in `sklearn`. In order to\n",
    "be consistent with the rest of this chapter, we use `lambdas`\n",
    "rather than `alphas` in what follows.  {At the time of publication, ridge fits like the one in code chunk [22] issue unwarranted convergence warning messages; we expect these to disappear as this package matures.}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "4a5d6fc8",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:27.250946Z",
     "iopub.status.busy": "2024-06-04T23:19:27.250878Z",
     "iopub.status.idle": "2024-06-04T23:19:27.303537Z",
     "shell.execute_reply": "2024-06-04T23:19:27.303273Z"
    },
    "lines_to_next_cell": 0
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(19, 100)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xs = X - X.mean(0)[None,:]\n",
    "X_scale = X.std(0)\n",
    "Xs = Xs / X_scale[None,:]\n",
    "lambdas = 10**np.linspace(8, -2, 100) / Y.std()\n",
    "soln_array = skl.ElasticNet.path(Xs,\n",
    "                                 Y,\n",
    "                                 l1_ratio=0.,\n",
    "                                 alphas=lambdas)[1]\n",
    "soln_array.shape\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e7770f5",
   "metadata": {},
   "source": [
    "Here we extract the array of coefficients corresponding to the solutions along the regularization path.\n",
    "By default the `skl.ElasticNet.path` method fits a path along\n",
    "an automatically selected range of $\\lambda$ values, except for the case when\n",
    "`l1_ratio=0`, which results in ridge regression (as is the case here). {The reason is rather technical; for all models except ridge, we can find the smallest value of $\\lambda$ for which all coefficients are zero. For ridge this value is $\\infty$.}  So here\n",
    "we have chosen to implement the function over a grid of values ranging\n",
    "from $\\lambda=10^{8}$ to $\\lambda=10^{-2}$ scaled by the standard\n",
    "deviation of $y$, essentially covering the full range of scenarios\n",
    "from the null model containing only the intercept, to the least\n",
    "squares fit.\n",
    "\n",
    "Associated with each value of $\\lambda$ is a vector of ridge\n",
    "regression coefficients,   that can be accessed by\n",
    "a column of `soln_array`. In this case, `soln_array` is a $19 \\times 100$ matrix, with\n",
    "19 rows (one for each predictor) and 100\n",
    "columns (one for each value of $\\lambda$).\n",
    "\n",
    "We transpose this matrix and turn it into a data frame to facilitate viewing and plotting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "1bca28f6",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:27.304830Z",
     "iopub.status.busy": "2024-06-04T23:19:27.304756Z",
     "iopub.status.idle": "2024-06-04T23:19:27.311709Z",
     "shell.execute_reply": "2024-06-04T23:19:27.311502Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AtBat</th>\n",
       "      <th>Hits</th>\n",
       "      <th>HmRun</th>\n",
       "      <th>Runs</th>\n",
       "      <th>RBI</th>\n",
       "      <th>Walks</th>\n",
       "      <th>Years</th>\n",
       "      <th>CAtBat</th>\n",
       "      <th>CHits</th>\n",
       "      <th>CHmRun</th>\n",
       "      <th>CRuns</th>\n",
       "      <th>CRBI</th>\n",
       "      <th>CWalks</th>\n",
       "      <th>League[N]</th>\n",
       "      <th>Division[W]</th>\n",
       "      <th>PutOuts</th>\n",
       "      <th>Assists</th>\n",
       "      <th>Errors</th>\n",
       "      <th>NewLeague[N]</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>negative log(lambda)</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>-12.310855</th>\n",
       "      <td>0.000800</td>\n",
       "      <td>0.000889</td>\n",
       "      <td>0.000695</td>\n",
       "      <td>0.000851</td>\n",
       "      <td>0.000911</td>\n",
       "      <td>0.000900</td>\n",
       "      <td>0.000812</td>\n",
       "      <td>0.001067</td>\n",
       "      <td>0.001113</td>\n",
       "      <td>0.001064</td>\n",
       "      <td>0.001141</td>\n",
       "      <td>0.001149</td>\n",
       "      <td>0.000993</td>\n",
       "      <td>-0.000029</td>\n",
       "      <td>-0.000390</td>\n",
       "      <td>0.000609</td>\n",
       "      <td>0.000052</td>\n",
       "      <td>-0.000011</td>\n",
       "      <td>-0.000006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-12.078271</th>\n",
       "      <td>0.001010</td>\n",
       "      <td>0.001122</td>\n",
       "      <td>0.000878</td>\n",
       "      <td>0.001074</td>\n",
       "      <td>0.001150</td>\n",
       "      <td>0.001135</td>\n",
       "      <td>0.001025</td>\n",
       "      <td>0.001346</td>\n",
       "      <td>0.001404</td>\n",
       "      <td>0.001343</td>\n",
       "      <td>0.001439</td>\n",
       "      <td>0.001450</td>\n",
       "      <td>0.001253</td>\n",
       "      <td>-0.000037</td>\n",
       "      <td>-0.000492</td>\n",
       "      <td>0.000769</td>\n",
       "      <td>0.000065</td>\n",
       "      <td>-0.000014</td>\n",
       "      <td>-0.000007</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-11.845686</th>\n",
       "      <td>0.001274</td>\n",
       "      <td>0.001416</td>\n",
       "      <td>0.001107</td>\n",
       "      <td>0.001355</td>\n",
       "      <td>0.001451</td>\n",
       "      <td>0.001433</td>\n",
       "      <td>0.001293</td>\n",
       "      <td>0.001698</td>\n",
       "      <td>0.001772</td>\n",
       "      <td>0.001694</td>\n",
       "      <td>0.001816</td>\n",
       "      <td>0.001830</td>\n",
       "      <td>0.001581</td>\n",
       "      <td>-0.000046</td>\n",
       "      <td>-0.000621</td>\n",
       "      <td>0.000970</td>\n",
       "      <td>0.000082</td>\n",
       "      <td>-0.000017</td>\n",
       "      <td>-0.000009</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-11.613102</th>\n",
       "      <td>0.001608</td>\n",
       "      <td>0.001787</td>\n",
       "      <td>0.001397</td>\n",
       "      <td>0.001710</td>\n",
       "      <td>0.001831</td>\n",
       "      <td>0.001808</td>\n",
       "      <td>0.001632</td>\n",
       "      <td>0.002143</td>\n",
       "      <td>0.002236</td>\n",
       "      <td>0.002138</td>\n",
       "      <td>0.002292</td>\n",
       "      <td>0.002309</td>\n",
       "      <td>0.001995</td>\n",
       "      <td>-0.000058</td>\n",
       "      <td>-0.000784</td>\n",
       "      <td>0.001224</td>\n",
       "      <td>0.000104</td>\n",
       "      <td>-0.000022</td>\n",
       "      <td>-0.000012</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-11.380518</th>\n",
       "      <td>0.002029</td>\n",
       "      <td>0.002255</td>\n",
       "      <td>0.001763</td>\n",
       "      <td>0.002158</td>\n",
       "      <td>0.002310</td>\n",
       "      <td>0.002281</td>\n",
       "      <td>0.002059</td>\n",
       "      <td>0.002704</td>\n",
       "      <td>0.002821</td>\n",
       "      <td>0.002698</td>\n",
       "      <td>0.002892</td>\n",
       "      <td>0.002914</td>\n",
       "      <td>0.002517</td>\n",
       "      <td>-0.000073</td>\n",
       "      <td>-0.000990</td>\n",
       "      <td>0.001544</td>\n",
       "      <td>0.000131</td>\n",
       "      <td>-0.000028</td>\n",
       "      <td>-0.000015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.784658</th>\n",
       "      <td>-290.823989</td>\n",
       "      <td>336.929968</td>\n",
       "      <td>37.322686</td>\n",
       "      <td>-59.748520</td>\n",
       "      <td>-26.507086</td>\n",
       "      <td>134.855915</td>\n",
       "      <td>-17.216195</td>\n",
       "      <td>-387.775826</td>\n",
       "      <td>89.573601</td>\n",
       "      <td>-12.273926</td>\n",
       "      <td>476.079273</td>\n",
       "      <td>257.271255</td>\n",
       "      <td>-213.124780</td>\n",
       "      <td>31.258215</td>\n",
       "      <td>-58.457857</td>\n",
       "      <td>78.761266</td>\n",
       "      <td>53.622113</td>\n",
       "      <td>-22.208456</td>\n",
       "      <td>-12.402891</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10.017243</th>\n",
       "      <td>-290.879272</td>\n",
       "      <td>337.113713</td>\n",
       "      <td>37.431373</td>\n",
       "      <td>-59.916820</td>\n",
       "      <td>-26.606957</td>\n",
       "      <td>134.900549</td>\n",
       "      <td>-17.108041</td>\n",
       "      <td>-388.458404</td>\n",
       "      <td>89.000707</td>\n",
       "      <td>-12.661459</td>\n",
       "      <td>477.031349</td>\n",
       "      <td>257.966790</td>\n",
       "      <td>-213.280891</td>\n",
       "      <td>31.256434</td>\n",
       "      <td>-58.448850</td>\n",
       "      <td>78.761240</td>\n",
       "      <td>53.645147</td>\n",
       "      <td>-22.198802</td>\n",
       "      <td>-12.391969</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10.249827</th>\n",
       "      <td>-290.923382</td>\n",
       "      <td>337.260446</td>\n",
       "      <td>37.518064</td>\n",
       "      <td>-60.051166</td>\n",
       "      <td>-26.686604</td>\n",
       "      <td>134.936136</td>\n",
       "      <td>-17.022194</td>\n",
       "      <td>-388.997470</td>\n",
       "      <td>88.537380</td>\n",
       "      <td>-12.971603</td>\n",
       "      <td>477.791860</td>\n",
       "      <td>258.523025</td>\n",
       "      <td>-213.405740</td>\n",
       "      <td>31.254958</td>\n",
       "      <td>-58.441682</td>\n",
       "      <td>78.761230</td>\n",
       "      <td>53.663357</td>\n",
       "      <td>-22.191071</td>\n",
       "      <td>-12.383205</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10.482412</th>\n",
       "      <td>-290.958537</td>\n",
       "      <td>337.377455</td>\n",
       "      <td>37.587122</td>\n",
       "      <td>-60.158256</td>\n",
       "      <td>-26.750044</td>\n",
       "      <td>134.964477</td>\n",
       "      <td>-16.954081</td>\n",
       "      <td>-389.423414</td>\n",
       "      <td>88.164178</td>\n",
       "      <td>-13.219329</td>\n",
       "      <td>478.398404</td>\n",
       "      <td>258.967059</td>\n",
       "      <td>-213.505412</td>\n",
       "      <td>31.253747</td>\n",
       "      <td>-58.435983</td>\n",
       "      <td>78.761230</td>\n",
       "      <td>53.677759</td>\n",
       "      <td>-22.184893</td>\n",
       "      <td>-12.376191</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10.714996</th>\n",
       "      <td>-290.986528</td>\n",
       "      <td>337.470648</td>\n",
       "      <td>37.642077</td>\n",
       "      <td>-60.243522</td>\n",
       "      <td>-26.800522</td>\n",
       "      <td>134.987027</td>\n",
       "      <td>-16.900054</td>\n",
       "      <td>-389.760135</td>\n",
       "      <td>87.864551</td>\n",
       "      <td>-13.416889</td>\n",
       "      <td>478.881540</td>\n",
       "      <td>259.321007</td>\n",
       "      <td>-213.584869</td>\n",
       "      <td>31.252760</td>\n",
       "      <td>-58.431454</td>\n",
       "      <td>78.761235</td>\n",
       "      <td>53.689152</td>\n",
       "      <td>-22.179964</td>\n",
       "      <td>-12.370587</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 19 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                           AtBat        Hits      HmRun       Runs        RBI  \\\n",
       "negative log(lambda)                                                            \n",
       "-12.310855              0.000800    0.000889   0.000695   0.000851   0.000911   \n",
       "-12.078271              0.001010    0.001122   0.000878   0.001074   0.001150   \n",
       "-11.845686              0.001274    0.001416   0.001107   0.001355   0.001451   \n",
       "-11.613102              0.001608    0.001787   0.001397   0.001710   0.001831   \n",
       "-11.380518              0.002029    0.002255   0.001763   0.002158   0.002310   \n",
       "...                          ...         ...        ...        ...        ...   \n",
       " 9.784658            -290.823989  336.929968  37.322686 -59.748520 -26.507086   \n",
       " 10.017243           -290.879272  337.113713  37.431373 -59.916820 -26.606957   \n",
       " 10.249827           -290.923382  337.260446  37.518064 -60.051166 -26.686604   \n",
       " 10.482412           -290.958537  337.377455  37.587122 -60.158256 -26.750044   \n",
       " 10.714996           -290.986528  337.470648  37.642077 -60.243522 -26.800522   \n",
       "\n",
       "                           Walks      Years      CAtBat      CHits     CHmRun  \\\n",
       "negative log(lambda)                                                            \n",
       "-12.310855              0.000900   0.000812    0.001067   0.001113   0.001064   \n",
       "-12.078271              0.001135   0.001025    0.001346   0.001404   0.001343   \n",
       "-11.845686              0.001433   0.001293    0.001698   0.001772   0.001694   \n",
       "-11.613102              0.001808   0.001632    0.002143   0.002236   0.002138   \n",
       "-11.380518              0.002281   0.002059    0.002704   0.002821   0.002698   \n",
       "...                          ...        ...         ...        ...        ...   \n",
       " 9.784658             134.855915 -17.216195 -387.775826  89.573601 -12.273926   \n",
       " 10.017243            134.900549 -17.108041 -388.458404  89.000707 -12.661459   \n",
       " 10.249827            134.936136 -17.022194 -388.997470  88.537380 -12.971603   \n",
       " 10.482412            134.964477 -16.954081 -389.423414  88.164178 -13.219329   \n",
       " 10.714996            134.987027 -16.900054 -389.760135  87.864551 -13.416889   \n",
       "\n",
       "                           CRuns        CRBI      CWalks  League[N]  \\\n",
       "negative log(lambda)                                                  \n",
       "-12.310855              0.001141    0.001149    0.000993  -0.000029   \n",
       "-12.078271              0.001439    0.001450    0.001253  -0.000037   \n",
       "-11.845686              0.001816    0.001830    0.001581  -0.000046   \n",
       "-11.613102              0.002292    0.002309    0.001995  -0.000058   \n",
       "-11.380518              0.002892    0.002914    0.002517  -0.000073   \n",
       "...                          ...         ...         ...        ...   \n",
       " 9.784658             476.079273  257.271255 -213.124780  31.258215   \n",
       " 10.017243            477.031349  257.966790 -213.280891  31.256434   \n",
       " 10.249827            477.791860  258.523025 -213.405740  31.254958   \n",
       " 10.482412            478.398404  258.967059 -213.505412  31.253747   \n",
       " 10.714996            478.881540  259.321007 -213.584869  31.252760   \n",
       "\n",
       "                      Division[W]    PutOuts    Assists     Errors  \\\n",
       "negative log(lambda)                                                 \n",
       "-12.310855              -0.000390   0.000609   0.000052  -0.000011   \n",
       "-12.078271              -0.000492   0.000769   0.000065  -0.000014   \n",
       "-11.845686              -0.000621   0.000970   0.000082  -0.000017   \n",
       "-11.613102              -0.000784   0.001224   0.000104  -0.000022   \n",
       "-11.380518              -0.000990   0.001544   0.000131  -0.000028   \n",
       "...                           ...        ...        ...        ...   \n",
       " 9.784658              -58.457857  78.761266  53.622113 -22.208456   \n",
       " 10.017243             -58.448850  78.761240  53.645147 -22.198802   \n",
       " 10.249827             -58.441682  78.761230  53.663357 -22.191071   \n",
       " 10.482412             -58.435983  78.761230  53.677759 -22.184893   \n",
       " 10.714996             -58.431454  78.761235  53.689152 -22.179964   \n",
       "\n",
       "                      NewLeague[N]  \n",
       "negative log(lambda)                \n",
       "-12.310855               -0.000006  \n",
       "-12.078271               -0.000007  \n",
       "-11.845686               -0.000009  \n",
       "-11.613102               -0.000012  \n",
       "-11.380518               -0.000015  \n",
       "...                            ...  \n",
       " 9.784658               -12.402891  \n",
       " 10.017243              -12.391969  \n",
       " 10.249827              -12.383205  \n",
       " 10.482412              -12.376191  \n",
       " 10.714996              -12.370587  \n",
       "\n",
       "[100 rows x 19 columns]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "soln_path = pd.DataFrame(soln_array.T,\n",
    "                         columns=D.columns,\n",
    "                         index=-np.log(lambdas))\n",
    "soln_path.index.name = 'negative log(lambda)'\n",
    "soln_path\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2246bb2b",
   "metadata": {},
   "source": [
    "We plot the paths to get a sense of how the coefficients vary with $\\lambda$.\n",
    "To control the location of the legend we first set `legend` to `False` in the\n",
    "plot method, adding it afterward with the `legend()` method of `ax`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "08bc997b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:27.312975Z",
     "iopub.status.busy": "2024-06-04T23:19:27.312908Z",
     "iopub.status.idle": "2024-06-04T23:19:27.473880Z",
     "shell.execute_reply": "2024-06-04T23:19:27.473585Z"
    },
    "lines_to_next_cell": 0
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "path_fig, ax = subplots(figsize=(8,8))\n",
    "soln_path.plot(ax=ax, legend=False)\n",
    "ax.set_xlabel('$-\\log(\\lambda)$', fontsize=20)\n",
    "ax.set_ylabel('Standardized coefficients', fontsize=20)\n",
    "ax.legend(loc='upper left');\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae73ca09",
   "metadata": {},
   "source": [
    "(We have used `latex` formatting in the horizontal label, in order to format the Greek $\\lambda$ appropriately.) \n",
    "We expect the coefficient estimates to be much smaller, in terms of\n",
    "$\\ell_2$ norm, when a large value of $\\lambda$ is used, as compared to\n",
    "when a small value of $\\lambda$ is used. (Recall that the  $\\ell_2$ norm is the square root of the sum of squared coefficient values.) We display  the coefficients at the $40$th step,\n",
    "where $\\lambda$ is 25.535."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "0f7359c7",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:27.475363Z",
     "iopub.status.busy": "2024-06-04T23:19:27.475242Z",
     "iopub.status.idle": "2024-06-04T23:19:27.477806Z",
     "shell.execute_reply": "2024-06-04T23:19:27.477534Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(25.53538897200662,\n",
       " AtBat           5.433750\n",
       " Hits            6.223582\n",
       " HmRun           4.585498\n",
       " Runs            5.880855\n",
       " RBI             6.195921\n",
       " Walks           6.277975\n",
       " Years           5.299767\n",
       " CAtBat          7.147501\n",
       " CHits           7.539495\n",
       " CHmRun          7.182344\n",
       " CRuns           7.728649\n",
       " CRBI            7.790702\n",
       " CWalks          6.592901\n",
       " League[N]       0.042445\n",
       " Division[W]    -3.107159\n",
       " PutOuts         4.605263\n",
       " Assists         0.378371\n",
       " Errors         -0.135196\n",
       " NewLeague[N]    0.150323\n",
       " Name: -3.240065292879872, dtype: float64)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta_hat = soln_path.loc[soln_path.index[39]]\n",
    "lambdas[39], beta_hat\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9baa8b00",
   "metadata": {},
   "source": [
    "Let’s compute the $\\ell_2$ norm of the standardized coefficients."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "d2984305",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:27.479160Z",
     "iopub.status.busy": "2024-06-04T23:19:27.479064Z",
     "iopub.status.idle": "2024-06-04T23:19:27.481153Z",
     "shell.execute_reply": "2024-06-04T23:19:27.480921Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.17061720144378"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(beta_hat)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5111fc6f",
   "metadata": {},
   "source": [
    "In contrast, here is the $\\ell_2$ norm when $\\lambda$ is 2.44e-01.\n",
    "Note the much larger $\\ell_2$ norm of the\n",
    "coefficients associated with this smaller value of $\\lambda$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "9a3424a4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:27.482508Z",
     "iopub.status.busy": "2024-06-04T23:19:27.482402Z",
     "iopub.status.idle": "2024-06-04T23:19:27.484554Z",
     "shell.execute_reply": "2024-06-04T23:19:27.484320Z"
    },
    "lines_to_next_cell": 0
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.24374766133488554, 160.42371017725839)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta_hat = soln_path.loc[soln_path.index[59]]\n",
    "lambdas[59], np.linalg.norm(beta_hat)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50239927",
   "metadata": {},
   "source": [
    "Above we normalized `X` upfront, and fit the ridge model using `Xs`.\n",
    "The `Pipeline()`  object\n",
    "in `sklearn` provides a clear way to separate feature\n",
    "normalization from the fitting of the ridge model itself."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "c864d25f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:27.485813Z",
     "iopub.status.busy": "2024-06-04T23:19:27.485727Z",
     "iopub.status.idle": "2024-06-04T23:19:27.495072Z",
     "shell.execute_reply": "2024-06-04T23:19:27.494829Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-1 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-1 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-1 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-1 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-1 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>Pipeline(steps=[(&#x27;scaler&#x27;, StandardScaler()),\n",
       "                (&#x27;ridge&#x27;, ElasticNet(alpha=0.24374766133488554, l1_ratio=0))])</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item sk-dashed-wrapped\"><div class=\"sk-label-container\"><div class=\"sk-label fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" ><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;Pipeline<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.pipeline.Pipeline.html\">?<span>Documentation for Pipeline</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>Pipeline(steps=[(&#x27;scaler&#x27;, StandardScaler()),\n",
       "                (&#x27;ridge&#x27;, ElasticNet(alpha=0.24374766133488554, l1_ratio=0))])</pre></div> </div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" ><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;StandardScaler<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.preprocessing.StandardScaler.html\">?<span>Documentation for StandardScaler</span></a></label><div class=\"sk-toggleable__content fitted\"><pre>StandardScaler()</pre></div> </div></div><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-3\" type=\"checkbox\" ><label for=\"sk-estimator-id-3\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;ElasticNet<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.linear_model.ElasticNet.html\">?<span>Documentation for ElasticNet</span></a></label><div class=\"sk-toggleable__content fitted\"><pre>ElasticNet(alpha=0.24374766133488554, l1_ratio=0)</pre></div> </div></div></div></div></div></div>"
      ],
      "text/plain": [
       "Pipeline(steps=[('scaler', StandardScaler()),\n",
       "                ('ridge', ElasticNet(alpha=0.24374766133488554, l1_ratio=0))])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge = skl.ElasticNet(alpha=lambdas[59], l1_ratio=0)\n",
    "scaler = StandardScaler(with_mean=True,  with_std=True)\n",
    "pipe = Pipeline(steps=[('scaler', scaler), ('ridge', ridge)])\n",
    "pipe.fit(X, Y)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71c8c514",
   "metadata": {},
   "source": [
    "We show that it gives the same $\\ell_2$ norm as in our previous fit on the standardized data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "8a07da6e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:27.496384Z",
     "iopub.status.busy": "2024-06-04T23:19:27.496277Z",
     "iopub.status.idle": "2024-06-04T23:19:27.498333Z",
     "shell.execute_reply": "2024-06-04T23:19:27.498078Z"
    },
    "lines_to_next_cell": 0
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "160.4237101772591"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(ridge.coef_)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a20ea7e",
   "metadata": {},
   "source": [
    " Notice that the operation `pipe.fit(X, Y)` above has changed the `ridge` object, and in particular has added attributes such as `coef_` that were not there before. \n",
    "### Estimating Test Error of Ridge Regression\n",
    "Choosing an *a priori* value of $\\lambda$ for ridge regression is\n",
    "difficult if not impossible. We will want to use the validation method\n",
    "or cross-validation to select the tuning parameter. The reader may not\n",
    "be surprised that the  `Pipeline()` approach can be used in\n",
    "`skm.cross_validate()` with either a validation method\n",
    "(i.e. `validation`) or $k$-fold cross-validation.\n",
    "\n",
    "We fix the random state of the splitter\n",
    "so that the results obtained will be reproducible."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "c10e3ae5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:27.499658Z",
     "iopub.status.busy": "2024-06-04T23:19:27.499553Z",
     "iopub.status.idle": "2024-06-04T23:19:27.505630Z",
     "shell.execute_reply": "2024-06-04T23:19:27.505369Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([134214.00419204])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "validation = skm.ShuffleSplit(n_splits=1,\n",
    "                              test_size=0.5,\n",
    "                              random_state=0)\n",
    "ridge.alpha = 0.01\n",
    "results = skm.cross_validate(ridge,\n",
    "                             X,\n",
    "                             Y,\n",
    "                             scoring='neg_mean_squared_error',\n",
    "                             cv=validation)\n",
    "-results['test_score']\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5f962ee",
   "metadata": {},
   "source": [
    "The test MSE is 1.342e+05.  Note\n",
    "that if we had instead simply fit a model with just an intercept, we\n",
    "would have predicted each test observation using the mean of the\n",
    "training observations. We can get the same result by fitting a ridge regression model\n",
    "with a *very* large value of $\\lambda$. Note that `1e10`\n",
    "means $10^{10}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "0df2b24d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:27.507058Z",
     "iopub.status.busy": "2024-06-04T23:19:27.506964Z",
     "iopub.status.idle": "2024-06-04T23:19:27.512846Z",
     "shell.execute_reply": "2024-06-04T23:19:27.512640Z"
    },
    "lines_to_next_cell": 0
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([231788.32155285])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge.alpha = 1e10\n",
    "results = skm.cross_validate(ridge,\n",
    "                             X,\n",
    "                             Y,\n",
    "                             scoring='neg_mean_squared_error',\n",
    "                             cv=validation)\n",
    "-results['test_score']\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e78a776c",
   "metadata": {},
   "source": [
    "Obviously choosing $\\lambda=0.01$ is arbitrary,  so we will  use cross-validation or the validation-set\n",
    "approach to choose the tuning parameter $\\lambda$.\n",
    "The object `GridSearchCV()`  allows exhaustive\n",
    "grid search to choose such a parameter.\n",
    "\n",
    "We first use the validation set method\n",
    "to choose $\\lambda$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "9b76df85",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:27.514070Z",
     "iopub.status.busy": "2024-06-04T23:19:27.514003Z",
     "iopub.status.idle": "2024-06-04T23:19:27.851311Z",
     "shell.execute_reply": "2024-06-04T23:19:27.851092Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-2 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-2 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-2 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-2 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-2 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-2 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-2 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-2 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-2 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-2 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-2 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>Pipeline(steps=[(&#x27;scaler&#x27;, StandardScaler()),\n",
       "                (&#x27;ridge&#x27;, ElasticNet(alpha=0.005899006046740856, l1_ratio=0))])</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item sk-dashed-wrapped\"><div class=\"sk-label-container\"><div class=\"sk-label fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-4\" type=\"checkbox\" ><label for=\"sk-estimator-id-4\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;Pipeline<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.pipeline.Pipeline.html\">?<span>Documentation for Pipeline</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>Pipeline(steps=[(&#x27;scaler&#x27;, StandardScaler()),\n",
       "                (&#x27;ridge&#x27;, ElasticNet(alpha=0.005899006046740856, l1_ratio=0))])</pre></div> </div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-5\" type=\"checkbox\" ><label for=\"sk-estimator-id-5\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;StandardScaler<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.preprocessing.StandardScaler.html\">?<span>Documentation for StandardScaler</span></a></label><div class=\"sk-toggleable__content fitted\"><pre>StandardScaler()</pre></div> </div></div><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-6\" type=\"checkbox\" ><label for=\"sk-estimator-id-6\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;ElasticNet<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.linear_model.ElasticNet.html\">?<span>Documentation for ElasticNet</span></a></label><div class=\"sk-toggleable__content fitted\"><pre>ElasticNet(alpha=0.005899006046740856, l1_ratio=0)</pre></div> </div></div></div></div></div></div>"
      ],
      "text/plain": [
       "Pipeline(steps=[('scaler', StandardScaler()),\n",
       "                ('ridge', ElasticNet(alpha=0.005899006046740856, l1_ratio=0))])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "param_grid = {'ridge__alpha': lambdas}\n",
    "grid = skm.GridSearchCV(pipe,\n",
    "                        param_grid,\n",
    "                        cv=validation,\n",
    "                        scoring='neg_mean_squared_error')\n",
    "grid.fit(X, Y)\n",
    "grid.best_params_['ridge__alpha']\n",
    "grid.best_estimator_\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9befd23e",
   "metadata": {},
   "source": [
    "Alternatively, we can use 5-fold cross-validation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "3e4c1b53",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:27.852563Z",
     "iopub.status.busy": "2024-06-04T23:19:27.852495Z",
     "iopub.status.idle": "2024-06-04T23:19:30.080670Z",
     "shell.execute_reply": "2024-06-04T23:19:30.080412Z"
    },
    "lines_to_next_cell": 0
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-3 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-3 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-3 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-3 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-3 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-3 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-3 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-3 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-3 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-3 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-3 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-3 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-3 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-3 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-3 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-3 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-3\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>Pipeline(steps=[(&#x27;scaler&#x27;, StandardScaler()),\n",
       "                (&#x27;ridge&#x27;, ElasticNet(alpha=0.01185247763144249, l1_ratio=0))])</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item sk-dashed-wrapped\"><div class=\"sk-label-container\"><div class=\"sk-label fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-7\" type=\"checkbox\" ><label for=\"sk-estimator-id-7\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;Pipeline<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.pipeline.Pipeline.html\">?<span>Documentation for Pipeline</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>Pipeline(steps=[(&#x27;scaler&#x27;, StandardScaler()),\n",
       "                (&#x27;ridge&#x27;, ElasticNet(alpha=0.01185247763144249, l1_ratio=0))])</pre></div> </div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-8\" type=\"checkbox\" ><label for=\"sk-estimator-id-8\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;StandardScaler<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.preprocessing.StandardScaler.html\">?<span>Documentation for StandardScaler</span></a></label><div class=\"sk-toggleable__content fitted\"><pre>StandardScaler()</pre></div> </div></div><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-9\" type=\"checkbox\" ><label for=\"sk-estimator-id-9\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;ElasticNet<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.linear_model.ElasticNet.html\">?<span>Documentation for ElasticNet</span></a></label><div class=\"sk-toggleable__content fitted\"><pre>ElasticNet(alpha=0.01185247763144249, l1_ratio=0)</pre></div> </div></div></div></div></div></div>"
      ],
      "text/plain": [
       "Pipeline(steps=[('scaler', StandardScaler()),\n",
       "                ('ridge', ElasticNet(alpha=0.01185247763144249, l1_ratio=0))])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grid = skm.GridSearchCV(pipe, \n",
    "                        param_grid,\n",
    "                        cv=kfold,\n",
    "                        scoring='neg_mean_squared_error')\n",
    "grid.fit(X, Y)\n",
    "grid.best_params_['ridge__alpha']\n",
    "grid.best_estimator_\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cae429da",
   "metadata": {},
   "source": [
    "Recall we set up the `kfold` object for 5-fold cross-validation on page~\\pageref{line:choos-among-models}. We now plot the cross-validated MSE as a function of $-\\log(\\lambda)$, which has shrinkage decreasing from left\n",
    "to right."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "39ff3251",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:30.082088Z",
     "iopub.status.busy": "2024-06-04T23:19:30.082012Z",
     "iopub.status.idle": "2024-06-04T23:19:30.194197Z",
     "shell.execute_reply": "2024-06-04T23:19:30.193921Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ridge_fig, ax = subplots(figsize=(8,8))\n",
    "ax.errorbar(-np.log(lambdas),\n",
    "            -grid.cv_results_['mean_test_score'],\n",
    "            yerr=grid.cv_results_['std_test_score'] / np.sqrt(K))\n",
    "ax.set_ylim([50000,250000])\n",
    "ax.set_xlabel('$-\\log(\\lambda)$', fontsize=20)\n",
    "ax.set_ylabel('Cross-validated MSE', fontsize=20);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "854e0c21",
   "metadata": {},
   "source": [
    "One can cross-validate different metrics to choose a parameter. The default\n",
    "metric for `skl.ElasticNet()` is test $R^2$.\n",
    "Let’s compare $R^2$ to MSE for cross-validation here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "766ab0b0",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:30.195678Z",
     "iopub.status.busy": "2024-06-04T23:19:30.195576Z",
     "iopub.status.idle": "2024-06-04T23:19:32.425386Z",
     "shell.execute_reply": "2024-06-04T23:19:32.425155Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-4 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-4 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-4 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-4 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-4 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-4 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-4 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-4 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-4 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-4 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-4 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-4 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-4 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-4 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-4 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-4 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-4 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-4\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>GridSearchCV(cv=KFold(n_splits=5, random_state=0, shuffle=True),\n",
       "             estimator=Pipeline(steps=[(&#x27;scaler&#x27;, StandardScaler()),\n",
       "                                       (&#x27;ridge&#x27;,\n",
       "                                        ElasticNet(alpha=10000000000.0,\n",
       "                                                   l1_ratio=0))]),\n",
       "             param_grid={&#x27;ridge__alpha&#x27;: array([2.22093791e+05, 1.76005531e+05, 1.39481373e+05, 1.10536603e+05,\n",
       "       8.75983676e+04, 6.94202082e+04, 5.50143278e+04, 4.35979140e+04,\n",
       "       3.45506012e+04, 2.73807606...\n",
       "       4.67486141e-03, 3.70474772e-03, 2.93594921e-03, 2.32668954e-03,\n",
       "       1.84386167e-03, 1.46122884e-03, 1.15799887e-03, 9.17694298e-04,\n",
       "       7.27257037e-04, 5.76338765e-04, 4.56738615e-04, 3.61957541e-04,\n",
       "       2.86845161e-04, 2.27319885e-04, 1.80147121e-04, 1.42763513e-04,\n",
       "       1.13137642e-04, 8.96596467e-05, 7.10537367e-05, 5.63088712e-05,\n",
       "       4.46238174e-05, 3.53636122e-05, 2.80250579e-05, 2.22093791e-05])})</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item sk-dashed-wrapped\"><div class=\"sk-label-container\"><div class=\"sk-label fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-10\" type=\"checkbox\" ><label for=\"sk-estimator-id-10\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;GridSearchCV<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.model_selection.GridSearchCV.html\">?<span>Documentation for GridSearchCV</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>GridSearchCV(cv=KFold(n_splits=5, random_state=0, shuffle=True),\n",
       "             estimator=Pipeline(steps=[(&#x27;scaler&#x27;, StandardScaler()),\n",
       "                                       (&#x27;ridge&#x27;,\n",
       "                                        ElasticNet(alpha=10000000000.0,\n",
       "                                                   l1_ratio=0))]),\n",
       "             param_grid={&#x27;ridge__alpha&#x27;: array([2.22093791e+05, 1.76005531e+05, 1.39481373e+05, 1.10536603e+05,\n",
       "       8.75983676e+04, 6.94202082e+04, 5.50143278e+04, 4.35979140e+04,\n",
       "       3.45506012e+04, 2.73807606...\n",
       "       4.67486141e-03, 3.70474772e-03, 2.93594921e-03, 2.32668954e-03,\n",
       "       1.84386167e-03, 1.46122884e-03, 1.15799887e-03, 9.17694298e-04,\n",
       "       7.27257037e-04, 5.76338765e-04, 4.56738615e-04, 3.61957541e-04,\n",
       "       2.86845161e-04, 2.27319885e-04, 1.80147121e-04, 1.42763513e-04,\n",
       "       1.13137642e-04, 8.96596467e-05, 7.10537367e-05, 5.63088712e-05,\n",
       "       4.46238174e-05, 3.53636122e-05, 2.80250579e-05, 2.22093791e-05])})</pre></div> </div></div><div class=\"sk-parallel\"><div class=\"sk-parallel-item\"><div class=\"sk-item\"><div class=\"sk-label-container\"><div class=\"sk-label fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-11\" type=\"checkbox\" ><label for=\"sk-estimator-id-11\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">best_estimator_: Pipeline</label><div class=\"sk-toggleable__content fitted\"><pre>Pipeline(steps=[(&#x27;scaler&#x27;, StandardScaler()),\n",
       "                (&#x27;ridge&#x27;, ElasticNet(alpha=0.01185247763144249, l1_ratio=0))])</pre></div> </div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-12\" type=\"checkbox\" ><label for=\"sk-estimator-id-12\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;StandardScaler<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.preprocessing.StandardScaler.html\">?<span>Documentation for StandardScaler</span></a></label><div class=\"sk-toggleable__content fitted\"><pre>StandardScaler()</pre></div> </div></div><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-13\" type=\"checkbox\" ><label for=\"sk-estimator-id-13\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;ElasticNet<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.linear_model.ElasticNet.html\">?<span>Documentation for ElasticNet</span></a></label><div class=\"sk-toggleable__content fitted\"><pre>ElasticNet(alpha=0.01185247763144249, l1_ratio=0)</pre></div> </div></div></div></div></div></div></div></div></div></div></div>"
      ],
      "text/plain": [
       "GridSearchCV(cv=KFold(n_splits=5, random_state=0, shuffle=True),\n",
       "             estimator=Pipeline(steps=[('scaler', StandardScaler()),\n",
       "                                       ('ridge',\n",
       "                                        ElasticNet(alpha=10000000000.0,\n",
       "                                                   l1_ratio=0))]),\n",
       "             param_grid={'ridge__alpha': array([2.22093791e+05, 1.76005531e+05, 1.39481373e+05, 1.10536603e+05,\n",
       "       8.75983676e+04, 6.94202082e+04, 5.50143278e+04, 4.35979140e+04,\n",
       "       3.45506012e+04, 2.73807606...\n",
       "       4.67486141e-03, 3.70474772e-03, 2.93594921e-03, 2.32668954e-03,\n",
       "       1.84386167e-03, 1.46122884e-03, 1.15799887e-03, 9.17694298e-04,\n",
       "       7.27257037e-04, 5.76338765e-04, 4.56738615e-04, 3.61957541e-04,\n",
       "       2.86845161e-04, 2.27319885e-04, 1.80147121e-04, 1.42763513e-04,\n",
       "       1.13137642e-04, 8.96596467e-05, 7.10537367e-05, 5.63088712e-05,\n",
       "       4.46238174e-05, 3.53636122e-05, 2.80250579e-05, 2.22093791e-05])})"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grid_r2 = skm.GridSearchCV(pipe, \n",
    "                           param_grid,\n",
    "                           cv=kfold)\n",
    "grid_r2.fit(X, Y)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3887a9c",
   "metadata": {},
   "source": [
    "Finally, let’s plot the results for cross-validated $R^2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "642f1de3",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:32.426644Z",
     "iopub.status.busy": "2024-06-04T23:19:32.426570Z",
     "iopub.status.idle": "2024-06-04T23:19:32.492503Z",
     "shell.execute_reply": "2024-06-04T23:19:32.492264Z"
    },
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r2_fig, ax = subplots(figsize=(8,8))\n",
    "ax.errorbar(-np.log(lambdas),\n",
    "            grid_r2.cv_results_['mean_test_score'],\n",
    "            yerr=grid_r2.cv_results_['std_test_score'] / np.sqrt(K))\n",
    "ax.set_xlabel('$-\\log(\\lambda)$', fontsize=20)\n",
    "ax.set_ylabel('Cross-validated $R^2$', fontsize=20);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0cb6f97b",
   "metadata": {},
   "source": [
    "### Fast Cross-Validation for Solution Paths\n",
    "The ridge, lasso, and elastic net can be efficiently fit along a sequence of $\\lambda$ values, creating what is known as a *solution path* or *regularization path*. Hence there is specialized code to fit\n",
    "such paths, and to choose a suitable value of $\\lambda$ using cross-validation. Even with\n",
    "identical splits the results will not agree *exactly* with our `grid`\n",
    "above because the standardization of each feature  in `grid` is carried out on each fold,\n",
    "while in `pipeCV` below it is carried out only once.\n",
    "Nevertheless, the results are similar as the normalization\n",
    "is relatively stable across folds."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "016ffe7c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:32.493853Z",
     "iopub.status.busy": "2024-06-04T23:19:32.493772Z",
     "iopub.status.idle": "2024-06-04T23:19:32.763066Z",
     "shell.execute_reply": "2024-06-04T23:19:32.762828Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-5 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-5 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-5 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-5 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-5 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-5 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-5 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-5 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-5 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-5 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-5 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-5 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-5 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-5 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-5 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-5 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-5 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-5\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>Pipeline(steps=[(&#x27;scaler&#x27;, StandardScaler()),\n",
       "                (&#x27;ridge&#x27;,\n",
       "                 ElasticNetCV(alphas=array([2.22093791e+05, 1.76005531e+05, 1.39481373e+05, 1.10536603e+05,\n",
       "       8.75983676e+04, 6.94202082e+04, 5.50143278e+04, 4.35979140e+04,\n",
       "       3.45506012e+04, 2.73807606e+04, 2.16987845e+04, 1.71959156e+04,\n",
       "       1.36274691e+04, 1.07995362e+04, 8.55844774e+03, 6.78242347e+03,\n",
       "       5.37495461e+03, 4.25955961e+03,...\n",
       "       1.84386167e-03, 1.46122884e-03, 1.15799887e-03, 9.17694298e-04,\n",
       "       7.27257037e-04, 5.76338765e-04, 4.56738615e-04, 3.61957541e-04,\n",
       "       2.86845161e-04, 2.27319885e-04, 1.80147121e-04, 1.42763513e-04,\n",
       "       1.13137642e-04, 8.96596467e-05, 7.10537367e-05, 5.63088712e-05,\n",
       "       4.46238174e-05, 3.53636122e-05, 2.80250579e-05, 2.22093791e-05]),\n",
       "                              cv=KFold(n_splits=5, random_state=0, shuffle=True),\n",
       "                              l1_ratio=0))])</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item sk-dashed-wrapped\"><div class=\"sk-label-container\"><div class=\"sk-label fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-14\" type=\"checkbox\" ><label for=\"sk-estimator-id-14\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;Pipeline<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.pipeline.Pipeline.html\">?<span>Documentation for Pipeline</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>Pipeline(steps=[(&#x27;scaler&#x27;, StandardScaler()),\n",
       "                (&#x27;ridge&#x27;,\n",
       "                 ElasticNetCV(alphas=array([2.22093791e+05, 1.76005531e+05, 1.39481373e+05, 1.10536603e+05,\n",
       "       8.75983676e+04, 6.94202082e+04, 5.50143278e+04, 4.35979140e+04,\n",
       "       3.45506012e+04, 2.73807606e+04, 2.16987845e+04, 1.71959156e+04,\n",
       "       1.36274691e+04, 1.07995362e+04, 8.55844774e+03, 6.78242347e+03,\n",
       "       5.37495461e+03, 4.25955961e+03,...\n",
       "       1.84386167e-03, 1.46122884e-03, 1.15799887e-03, 9.17694298e-04,\n",
       "       7.27257037e-04, 5.76338765e-04, 4.56738615e-04, 3.61957541e-04,\n",
       "       2.86845161e-04, 2.27319885e-04, 1.80147121e-04, 1.42763513e-04,\n",
       "       1.13137642e-04, 8.96596467e-05, 7.10537367e-05, 5.63088712e-05,\n",
       "       4.46238174e-05, 3.53636122e-05, 2.80250579e-05, 2.22093791e-05]),\n",
       "                              cv=KFold(n_splits=5, random_state=0, shuffle=True),\n",
       "                              l1_ratio=0))])</pre></div> </div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-15\" type=\"checkbox\" ><label for=\"sk-estimator-id-15\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;StandardScaler<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.preprocessing.StandardScaler.html\">?<span>Documentation for StandardScaler</span></a></label><div class=\"sk-toggleable__content fitted\"><pre>StandardScaler()</pre></div> </div></div><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-16\" type=\"checkbox\" ><label for=\"sk-estimator-id-16\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;ElasticNetCV<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.linear_model.ElasticNetCV.html\">?<span>Documentation for ElasticNetCV</span></a></label><div class=\"sk-toggleable__content fitted\"><pre>ElasticNetCV(alphas=array([2.22093791e+05, 1.76005531e+05, 1.39481373e+05, 1.10536603e+05,\n",
       "       8.75983676e+04, 6.94202082e+04, 5.50143278e+04, 4.35979140e+04,\n",
       "       3.45506012e+04, 2.73807606e+04, 2.16987845e+04, 1.71959156e+04,\n",
       "       1.36274691e+04, 1.07995362e+04, 8.55844774e+03, 6.78242347e+03,\n",
       "       5.37495461e+03, 4.25955961e+03, 3.37562814e+03, 2.67512757e+03,\n",
       "       2.11999285e+03, 1.680058...\n",
       "       1.84386167e-03, 1.46122884e-03, 1.15799887e-03, 9.17694298e-04,\n",
       "       7.27257037e-04, 5.76338765e-04, 4.56738615e-04, 3.61957541e-04,\n",
       "       2.86845161e-04, 2.27319885e-04, 1.80147121e-04, 1.42763513e-04,\n",
       "       1.13137642e-04, 8.96596467e-05, 7.10537367e-05, 5.63088712e-05,\n",
       "       4.46238174e-05, 3.53636122e-05, 2.80250579e-05, 2.22093791e-05]),\n",
       "             cv=KFold(n_splits=5, random_state=0, shuffle=True), l1_ratio=0)</pre></div> </div></div></div></div></div></div>"
      ],
      "text/plain": [
       "Pipeline(steps=[('scaler', StandardScaler()),\n",
       "                ('ridge',\n",
       "                 ElasticNetCV(alphas=array([2.22093791e+05, 1.76005531e+05, 1.39481373e+05, 1.10536603e+05,\n",
       "       8.75983676e+04, 6.94202082e+04, 5.50143278e+04, 4.35979140e+04,\n",
       "       3.45506012e+04, 2.73807606e+04, 2.16987845e+04, 1.71959156e+04,\n",
       "       1.36274691e+04, 1.07995362e+04, 8.55844774e+03, 6.78242347e+03,\n",
       "       5.37495461e+03, 4.25955961e+03,...\n",
       "       1.84386167e-03, 1.46122884e-03, 1.15799887e-03, 9.17694298e-04,\n",
       "       7.27257037e-04, 5.76338765e-04, 4.56738615e-04, 3.61957541e-04,\n",
       "       2.86845161e-04, 2.27319885e-04, 1.80147121e-04, 1.42763513e-04,\n",
       "       1.13137642e-04, 8.96596467e-05, 7.10537367e-05, 5.63088712e-05,\n",
       "       4.46238174e-05, 3.53636122e-05, 2.80250579e-05, 2.22093791e-05]),\n",
       "                              cv=KFold(n_splits=5, random_state=0, shuffle=True),\n",
       "                              l1_ratio=0))])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridgeCV = skl.ElasticNetCV(alphas=lambdas, \n",
    "                           l1_ratio=0,\n",
    "                           cv=kfold)\n",
    "pipeCV = Pipeline(steps=[('scaler', scaler),\n",
    "                         ('ridge', ridgeCV)])\n",
    "pipeCV.fit(X, Y)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6845efe",
   "metadata": {},
   "source": [
    "Let’s produce a plot again of the cross-validation error to see that\n",
    "it is similar to using `skm.GridSearchCV`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "52f6cf29",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:32.764408Z",
     "iopub.status.busy": "2024-06-04T23:19:32.764316Z",
     "iopub.status.idle": "2024-06-04T23:19:32.836546Z",
     "shell.execute_reply": "2024-06-04T23:19:32.836313Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tuned_ridge = pipeCV.named_steps['ridge']\n",
    "ridgeCV_fig, ax = subplots(figsize=(8,8))\n",
    "ax.errorbar(-np.log(lambdas),\n",
    "            tuned_ridge.mse_path_.mean(1),\n",
    "            yerr=tuned_ridge.mse_path_.std(1) / np.sqrt(K))\n",
    "ax.axvline(-np.log(tuned_ridge.alpha_), c='k', ls='--')\n",
    "ax.set_ylim([50000,250000])\n",
    "ax.set_xlabel('$-\\log(\\lambda)$', fontsize=20)\n",
    "ax.set_ylabel('Cross-validated MSE', fontsize=20);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80e07995",
   "metadata": {},
   "source": [
    "We see that the value of $\\lambda$ that results in the\n",
    "smallest cross-validation error is 1.19e-02, available\n",
    "as the value `tuned_ridge.alpha_`. What is the test MSE\n",
    "associated with this value of $\\lambda$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "2b49c3d7",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:32.838011Z",
     "iopub.status.busy": "2024-06-04T23:19:32.837899Z",
     "iopub.status.idle": "2024-06-04T23:19:32.840000Z",
     "shell.execute_reply": "2024-06-04T23:19:32.839740Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "115526.70630987917"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.min(tuned_ridge.mse_path_.mean(1))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0961957c",
   "metadata": {},
   "source": [
    "This represents a further improvement over the test MSE that we got\n",
    "using $\\lambda=4$.  Finally, `tuned_ridge.coef_`\n",
    "has the coefficients fit on the entire data set\n",
    "at this value of  $\\lambda$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "973e7e79",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:32.841440Z",
     "iopub.status.busy": "2024-06-04T23:19:32.841345Z",
     "iopub.status.idle": "2024-06-04T23:19:32.843427Z",
     "shell.execute_reply": "2024-06-04T23:19:32.843185Z"
    },
    "lines_to_next_cell": 0
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-222.80877051,  238.77246614,    3.21103754,   -2.93050845,\n",
       "          3.64888723,  108.90953869,  -50.81896152, -105.15731984,\n",
       "        122.00714801,   57.1859509 ,  210.35170348,  118.05683748,\n",
       "       -150.21959435,   30.36634231,  -61.62459095,   77.73832472,\n",
       "         40.07350744,  -25.02151514,  -13.68429544])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tuned_ridge.coef_\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b19ffa3f",
   "metadata": {},
   "source": [
    "As expected, none of the coefficients are zero—ridge regression does\n",
    "not perform variable selection!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bfb6c72e",
   "metadata": {},
   "source": [
    "### Evaluating Test Error of Cross-Validated Ridge\n",
    "Choosing $\\lambda$ using cross-validation provides a single regression\n",
    "estimator, similar to fitting a linear regression model as we saw in\n",
    "Chapter~\\ref{Ch3:linreg}. It is therefore reasonable to estimate what its test error\n",
    "is. We run into a problem here in that cross-validation will have\n",
    "*touched* all of its data in choosing $\\lambda$, hence we have no\n",
    "further data to estimate test error. A compromise is to do an initial\n",
    "split of the data into two disjoint sets: a training set and a test set.\n",
    "We then fit a cross-validation\n",
    "tuned ridge regression on the training set, and evaluate its performance on the test set.\n",
    "We might call this cross-validation nested\n",
    "within the validation set approach. A priori there is no reason to use\n",
    "half of the data for each of the two sets in validation. Below, we use\n",
    "75% for training and 25% for test, with the estimator being ridge\n",
    "regression tuned using 5-fold cross-validation.  This can be achieved\n",
    "in code as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "a9140b3a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:32.844819Z",
     "iopub.status.busy": "2024-06-04T23:19:32.844727Z",
     "iopub.status.idle": "2024-06-04T23:19:32.846512Z",
     "shell.execute_reply": "2024-06-04T23:19:32.846267Z"
    }
   },
   "outputs": [],
   "source": [
    "outer_valid = skm.ShuffleSplit(n_splits=1, \n",
    "                               test_size=0.25,\n",
    "                               random_state=1)\n",
    "inner_cv = skm.KFold(n_splits=5,\n",
    "                     shuffle=True,\n",
    "                     random_state=2)\n",
    "ridgeCV = skl.ElasticNetCV(alphas=lambdas,\n",
    "                           l1_ratio=0,\n",
    "                           cv=inner_cv)\n",
    "pipeCV = Pipeline(steps=[('scaler', scaler),\n",
    "                         ('ridge', ridgeCV)]);\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "8fc4aea0",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:32.847712Z",
     "iopub.status.busy": "2024-06-04T23:19:32.847645Z",
     "iopub.status.idle": "2024-06-04T23:19:33.096196Z",
     "shell.execute_reply": "2024-06-04T23:19:33.095971Z"
    },
    "lines_to_next_cell": 0
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([132393.84003227])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results = skm.cross_validate(pipeCV, \n",
    "                             X,\n",
    "                             Y,\n",
    "                             cv=outer_valid,\n",
    "                             scoring='neg_mean_squared_error')\n",
    "-results['test_score']\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e27147ec",
   "metadata": {},
   "source": [
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4f126e9",
   "metadata": {},
   "source": [
    "### The Lasso\n",
    "We saw that ridge regression with a wise choice of $\\lambda$ can\n",
    "outperform least squares as well as the null model on the\n",
    " `Hitters`  data set. We now ask whether the lasso can yield\n",
    "either a more accurate or a more interpretable model than ridge\n",
    "regression. In order to fit a lasso model, we once again use the\n",
    "`ElasticNetCV()`  function; however, this time we use the argument\n",
    "`l1_ratio=1`. Other than that change, we proceed just as we did in\n",
    "fitting a ridge model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "008ecc7c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:33.097496Z",
     "iopub.status.busy": "2024-06-04T23:19:33.097429Z",
     "iopub.status.idle": "2024-06-04T23:19:33.139203Z",
     "shell.execute_reply": "2024-06-04T23:19:33.138992Z"
    },
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.1472370031649866"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lassoCV = skl.ElasticNetCV(n_alphas=100, \n",
    "                           l1_ratio=1,\n",
    "                           cv=kfold)\n",
    "pipeCV = Pipeline(steps=[('scaler', scaler),\n",
    "                         ('lasso', lassoCV)])\n",
    "pipeCV.fit(X, Y)\n",
    "tuned_lasso = pipeCV.named_steps['lasso']\n",
    "tuned_lasso.alpha_\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "1b909861",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:33.140345Z",
     "iopub.status.busy": "2024-06-04T23:19:33.140279Z",
     "iopub.status.idle": "2024-06-04T23:19:33.148367Z",
     "shell.execute_reply": "2024-06-04T23:19:33.148166Z"
    },
    "lines_to_next_cell": 0
   },
   "outputs": [],
   "source": [
    "lambdas, soln_array = skl.Lasso.path(Xs, \n",
    "                                    Y,\n",
    "                                    l1_ratio=1,\n",
    "                                    n_alphas=100)[:2]\n",
    "soln_path = pd.DataFrame(soln_array.T,\n",
    "                         columns=D.columns,\n",
    "                         index=-np.log(lambdas))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "abec44b3",
   "metadata": {},
   "source": [
    "We can see from the coefficient plot of the standardized coefficients that depending on the choice of\n",
    "tuning parameter, some of the coefficients will be exactly equal to\n",
    "zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "ff719798",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:33.149542Z",
     "iopub.status.busy": "2024-06-04T23:19:33.149477Z",
     "iopub.status.idle": "2024-06-04T23:19:33.268439Z",
     "shell.execute_reply": "2024-06-04T23:19:33.268204Z"
    },
    "lines_to_next_cell": 0
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "path_fig, ax = subplots(figsize=(8,8))\n",
    "soln_path.plot(ax=ax, legend=False)\n",
    "ax.legend(loc='upper left')\n",
    "ax.set_xlabel('$-\\log(\\lambda)$', fontsize=20)\n",
    "ax.set_ylabel('Standardized coefficiients', fontsize=20);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "201ccdfb",
   "metadata": {},
   "source": [
    "The smallest cross-validated error is lower than the test set MSE of the null model\n",
    "and of least squares, and very similar to the test MSE of 115526.71 of ridge\n",
    "regression (page~\\pageref{page:MSECVRidge}) with $\\lambda$ chosen by cross-validation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "f21ad8dc",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:33.269744Z",
     "iopub.status.busy": "2024-06-04T23:19:33.269654Z",
     "iopub.status.idle": "2024-06-04T23:19:33.271587Z",
     "shell.execute_reply": "2024-06-04T23:19:33.271375Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "114690.73118253727"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.min(tuned_lasso.mse_path_.mean(1))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "136f171f",
   "metadata": {},
   "source": [
    "Let’s again produce a plot of the cross-validation error.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "7624e483",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:33.272793Z",
     "iopub.status.busy": "2024-06-04T23:19:33.272706Z",
     "iopub.status.idle": "2024-06-04T23:19:33.345703Z",
     "shell.execute_reply": "2024-06-04T23:19:33.345426Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lassoCV_fig, ax = subplots(figsize=(8,8))\n",
    "ax.errorbar(-np.log(tuned_lasso.alphas_),\n",
    "            tuned_lasso.mse_path_.mean(1),\n",
    "            yerr=tuned_lasso.mse_path_.std(1) / np.sqrt(K))\n",
    "ax.axvline(-np.log(tuned_lasso.alpha_), c='k', ls='--')\n",
    "ax.set_ylim([50000,250000])\n",
    "ax.set_xlabel('$-\\log(\\lambda)$', fontsize=20)\n",
    "ax.set_ylabel('Cross-validated MSE', fontsize=20);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2b85ea4",
   "metadata": {},
   "source": [
    "However, the lasso has a substantial advantage over ridge regression\n",
    "in that the resulting coefficient estimates are sparse. Here we see\n",
    "that 6 of the 19 coefficient estimates are exactly zero. So the lasso\n",
    "model with $\\lambda$ chosen by cross-validation contains only 13\n",
    "variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "b389c7d4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:33.347189Z",
     "iopub.status.busy": "2024-06-04T23:19:33.347081Z",
     "iopub.status.idle": "2024-06-04T23:19:33.349101Z",
     "shell.execute_reply": "2024-06-04T23:19:33.348883Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-210.01008773,  243.4550306 ,    0.        ,    0.        ,\n",
       "          0.        ,   97.69397357,  -41.52283116,   -0.        ,\n",
       "          0.        ,   39.62298193,  205.75273856,  124.55456561,\n",
       "       -126.29986768,   15.70262427,  -59.50157967,   75.24590036,\n",
       "         21.62698014,  -12.04423675,   -0.        ])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tuned_lasso.coef_\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "acc5ed38",
   "metadata": {},
   "source": [
    "As in ridge regression, we could evaluate the test error\n",
    "of cross-validated lasso by first splitting into\n",
    "test and training sets and internally running\n",
    "cross-validation on the training set. We leave\n",
    "this as an exercise."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d0aca26",
   "metadata": {},
   "source": [
    "## PCR and PLS Regression\n",
    "\n",
    "### Principal Components Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2120ab5",
   "metadata": {},
   "source": [
    "Principal components regression (PCR) can be performed using\n",
    "`PCA()`  from the `sklearn.decomposition`\n",
    "module. We now apply PCR to the  `Hitters`  data, in order to\n",
    "predict `Salary`. Again, ensure that the missing values have\n",
    "been removed from the data, as described in Section~\\ref{Ch6-varselect-lab:lab-1-subset-selection-methods}.\n",
    "\n",
    "We use `LinearRegression()`  to fit the regression model\n",
    "here. Note that it fits an intercept by default, unlike\n",
    "the `OLS()` function seen earlier in Section~\\ref{Ch6-varselect-lab:lab-1-subset-selection-methods}."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "cf302d4c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:33.350411Z",
     "iopub.status.busy": "2024-06-04T23:19:33.350323Z",
     "iopub.status.idle": "2024-06-04T23:19:33.353307Z",
     "shell.execute_reply": "2024-06-04T23:19:33.353084Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.09846131, 0.4758765 ])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA(n_components=2)\n",
    "linreg = skl.LinearRegression()\n",
    "pipe = Pipeline([('pca', pca),\n",
    "                 ('linreg', linreg)])\n",
    "pipe.fit(X, Y)\n",
    "pipe.named_steps['linreg'].coef_\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b909182b",
   "metadata": {},
   "source": [
    "When performing PCA, the results vary depending\n",
    "on whether the data has been *standardized* or not.\n",
    "As in the earlier examples, this can be accomplished\n",
    "by including an additional step in the pipeline."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "af4145b6",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:33.354462Z",
     "iopub.status.busy": "2024-06-04T23:19:33.354377Z",
     "iopub.status.idle": "2024-06-04T23:19:33.357347Z",
     "shell.execute_reply": "2024-06-04T23:19:33.357140Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([106.36859204,  21.60350456])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe = Pipeline([('scaler', scaler), \n",
    "                 ('pca', pca),\n",
    "                 ('linreg', linreg)])\n",
    "pipe.fit(X, Y)\n",
    "pipe.named_steps['linreg'].coef_\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0da4ae12",
   "metadata": {},
   "source": [
    "We can of course use CV to choose the number of components, by\n",
    "using `skm.GridSearchCV`, in this\n",
    "case fixing the parameters to vary the\n",
    "`n_components`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "16e047ed",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:33.358664Z",
     "iopub.status.busy": "2024-06-04T23:19:33.358558Z",
     "iopub.status.idle": "2024-06-04T23:19:33.448710Z",
     "shell.execute_reply": "2024-06-04T23:19:33.448481Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-6 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-6 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-6 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-6 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-6 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-6 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-6 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-6 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-6 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-6 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-6 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-6 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-6 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-6 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-6 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-6 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-6 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-6 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-6 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-6 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-6 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-6 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-6 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-6 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-6 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-6 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-6 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-6 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-6 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-6 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-6 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-6 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-6 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-6 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-6 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-6 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-6 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-6 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-6 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-6 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-6 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-6 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-6\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>GridSearchCV(cv=KFold(n_splits=5, random_state=0, shuffle=True),\n",
       "             estimator=Pipeline(steps=[(&#x27;scaler&#x27;, StandardScaler()),\n",
       "                                       (&#x27;pca&#x27;, PCA(n_components=2)),\n",
       "                                       (&#x27;linreg&#x27;, LinearRegression())]),\n",
       "             param_grid={&#x27;pca__n_components&#x27;: range(1, 20)},\n",
       "             scoring=&#x27;neg_mean_squared_error&#x27;)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item sk-dashed-wrapped\"><div class=\"sk-label-container\"><div class=\"sk-label fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-17\" type=\"checkbox\" ><label for=\"sk-estimator-id-17\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;GridSearchCV<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.model_selection.GridSearchCV.html\">?<span>Documentation for GridSearchCV</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>GridSearchCV(cv=KFold(n_splits=5, random_state=0, shuffle=True),\n",
       "             estimator=Pipeline(steps=[(&#x27;scaler&#x27;, StandardScaler()),\n",
       "                                       (&#x27;pca&#x27;, PCA(n_components=2)),\n",
       "                                       (&#x27;linreg&#x27;, LinearRegression())]),\n",
       "             param_grid={&#x27;pca__n_components&#x27;: range(1, 20)},\n",
       "             scoring=&#x27;neg_mean_squared_error&#x27;)</pre></div> </div></div><div class=\"sk-parallel\"><div class=\"sk-parallel-item\"><div class=\"sk-item\"><div class=\"sk-label-container\"><div class=\"sk-label fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-18\" type=\"checkbox\" ><label for=\"sk-estimator-id-18\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">best_estimator_: Pipeline</label><div class=\"sk-toggleable__content fitted\"><pre>Pipeline(steps=[(&#x27;scaler&#x27;, StandardScaler()), (&#x27;pca&#x27;, PCA(n_components=17)),\n",
       "                (&#x27;linreg&#x27;, LinearRegression())])</pre></div> </div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-19\" type=\"checkbox\" ><label for=\"sk-estimator-id-19\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;StandardScaler<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.preprocessing.StandardScaler.html\">?<span>Documentation for StandardScaler</span></a></label><div class=\"sk-toggleable__content fitted\"><pre>StandardScaler()</pre></div> </div></div><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-20\" type=\"checkbox\" ><label for=\"sk-estimator-id-20\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;PCA<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.decomposition.PCA.html\">?<span>Documentation for PCA</span></a></label><div class=\"sk-toggleable__content fitted\"><pre>PCA(n_components=17)</pre></div> </div></div><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-21\" type=\"checkbox\" ><label for=\"sk-estimator-id-21\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;LinearRegression<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.linear_model.LinearRegression.html\">?<span>Documentation for LinearRegression</span></a></label><div class=\"sk-toggleable__content fitted\"><pre>LinearRegression()</pre></div> </div></div></div></div></div></div></div></div></div></div></div>"
      ],
      "text/plain": [
       "GridSearchCV(cv=KFold(n_splits=5, random_state=0, shuffle=True),\n",
       "             estimator=Pipeline(steps=[('scaler', StandardScaler()),\n",
       "                                       ('pca', PCA(n_components=2)),\n",
       "                                       ('linreg', LinearRegression())]),\n",
       "             param_grid={'pca__n_components': range(1, 20)},\n",
       "             scoring='neg_mean_squared_error')"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "param_grid = {'pca__n_components': range(1, 20)}\n",
    "grid = skm.GridSearchCV(pipe,\n",
    "                        param_grid,\n",
    "                        cv=kfold,\n",
    "                        scoring='neg_mean_squared_error')\n",
    "grid.fit(X, Y)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "148bf752",
   "metadata": {},
   "source": [
    "Let’s plot the results as we have for other methods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "7390847f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:33.450064Z",
     "iopub.status.busy": "2024-06-04T23:19:33.449993Z",
     "iopub.status.idle": "2024-06-04T23:19:33.518771Z",
     "shell.execute_reply": "2024-06-04T23:19:33.518504Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pcr_fig, ax = subplots(figsize=(8,8))\n",
    "n_comp = param_grid['pca__n_components']\n",
    "ax.errorbar(n_comp,\n",
    "            -grid.cv_results_['mean_test_score'],\n",
    "            grid.cv_results_['std_test_score'] / np.sqrt(K))\n",
    "ax.set_ylabel('Cross-validated MSE', fontsize=20)\n",
    "ax.set_xlabel('# principal components', fontsize=20)\n",
    "ax.set_xticks(n_comp[::2])\n",
    "ax.set_ylim([50000,250000]);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4269a0db",
   "metadata": {},
   "source": [
    "We see that the smallest cross-validation error occurs when\n",
    "17\n",
    "components are used. However, from the plot we also see that the\n",
    "cross-validation error is roughly the same when only one component is\n",
    "included in the model. This suggests that a model that uses just a\n",
    "small number of components might suffice.\n",
    "\n",
    "The CV score is provided for each possible number of components from\n",
    "1 to 19 inclusive. The `PCA()` method complains\n",
    "if we try to fit an intercept only with `n_components=0`\n",
    "so we also compute the MSE for just the null model with\n",
    "these splits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "1e084cbb",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:33.520137Z",
     "iopub.status.busy": "2024-06-04T23:19:33.520059Z",
     "iopub.status.idle": "2024-06-04T23:19:33.525293Z",
     "shell.execute_reply": "2024-06-04T23:19:33.525077Z"
    },
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "204139.30692994667"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xn = np.zeros((X.shape[0], 1))\n",
    "cv_null = skm.cross_validate(linreg,\n",
    "                             Xn,\n",
    "                             Y,\n",
    "                             cv=kfold,\n",
    "                             scoring='neg_mean_squared_error')\n",
    "-cv_null['test_score'].mean()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c0d69df",
   "metadata": {},
   "source": [
    "The `explained_variance_ratio_`\n",
    "attribute of our `PCA` object provides the *percentage of variance explained* in the predictors and in the response using\n",
    "different numbers of components. This concept is discussed in greater\n",
    "detail in Section~\\ref{Ch10:sec:pca}."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "c7616c02",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:33.526523Z",
     "iopub.status.busy": "2024-06-04T23:19:33.526454Z",
     "iopub.status.idle": "2024-06-04T23:19:33.528563Z",
     "shell.execute_reply": "2024-06-04T23:19:33.528353Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.3831424 , 0.21841076])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe.named_steps['pca'].explained_variance_ratio_\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2ee7cb1",
   "metadata": {},
   "source": [
    "Briefly, we can think of\n",
    "this as the amount of information about the predictors\n",
    "that is captured using $M$ principal components. For example, setting\n",
    "$M=1$ only captures 38.31% of the variance, while $M=2$ captures an additional 21.84%, for a total of 60.15% of the variance.\n",
    "By  $M=6$ it increases to\n",
    "88.63%. Beyond this the increments continue to diminish, until we use all $M=p=19$ components, which captures all  100% of the variance.\n",
    "\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a0ce7e4",
   "metadata": {},
   "source": [
    "### Partial Least Squares\n",
    "Partial least squares (PLS) is implemented in the\n",
    "`PLSRegression()`  function.\n",
    "\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "9c69429e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:33.529851Z",
     "iopub.status.busy": "2024-06-04T23:19:33.529780Z",
     "iopub.status.idle": "2024-06-04T23:19:33.532907Z",
     "shell.execute_reply": "2024-06-04T23:19:33.532670Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-7 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-7 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-7 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-7 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-7 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-7 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-7 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-7 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-7 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-7 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-7 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-7 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-7 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-7 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-7 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-7 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-7 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-7 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-7 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-7 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-7 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-7 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-7 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-7 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-7 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-7 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-7 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-7 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-7 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-7 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-7 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-7 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-7 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-7 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-7 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-7 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-7 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-7 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-7 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-7 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-7 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-7 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-7\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>PLSRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-22\" type=\"checkbox\" checked><label for=\"sk-estimator-id-22\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;PLSRegression<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.cross_decomposition.PLSRegression.html\">?<span>Documentation for PLSRegression</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>PLSRegression()</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "PLSRegression()"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pls = PLSRegression(n_components=2, \n",
    "                    scale=True)\n",
    "pls.fit(X, Y)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a00592ba",
   "metadata": {},
   "source": [
    "As was the case in PCR, we will want to\n",
    "use CV to choose the number of components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "043f27fa",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:33.534240Z",
     "iopub.status.busy": "2024-06-04T23:19:33.534173Z",
     "iopub.status.idle": "2024-06-04T23:19:33.610294Z",
     "shell.execute_reply": "2024-06-04T23:19:33.610076Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-8 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-8 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-8 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-8 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-8 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-8 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-8 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-8 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-8 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-8 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-8 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-8 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-8 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-8 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-8 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-8 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-8 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-8 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-8 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-8 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-8 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-8 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-8 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-8 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-8 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-8 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-8 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-8 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-8 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-8 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-8 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-8 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-8 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-8 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-8 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-8 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-8 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-8 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-8 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-8 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-8 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-8 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-8\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>GridSearchCV(cv=KFold(n_splits=5, random_state=0, shuffle=True),\n",
       "             estimator=PLSRegression(),\n",
       "             param_grid={&#x27;n_components&#x27;: range(1, 20)},\n",
       "             scoring=&#x27;neg_mean_squared_error&#x27;)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item sk-dashed-wrapped\"><div class=\"sk-label-container\"><div class=\"sk-label fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-23\" type=\"checkbox\" ><label for=\"sk-estimator-id-23\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;GridSearchCV<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.model_selection.GridSearchCV.html\">?<span>Documentation for GridSearchCV</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>GridSearchCV(cv=KFold(n_splits=5, random_state=0, shuffle=True),\n",
       "             estimator=PLSRegression(),\n",
       "             param_grid={&#x27;n_components&#x27;: range(1, 20)},\n",
       "             scoring=&#x27;neg_mean_squared_error&#x27;)</pre></div> </div></div><div class=\"sk-parallel\"><div class=\"sk-parallel-item\"><div class=\"sk-item\"><div class=\"sk-label-container\"><div class=\"sk-label fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-24\" type=\"checkbox\" ><label for=\"sk-estimator-id-24\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">best_estimator_: PLSRegression</label><div class=\"sk-toggleable__content fitted\"><pre>PLSRegression(n_components=12)</pre></div> </div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-25\" type=\"checkbox\" ><label for=\"sk-estimator-id-25\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;PLSRegression<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.cross_decomposition.PLSRegression.html\">?<span>Documentation for PLSRegression</span></a></label><div class=\"sk-toggleable__content fitted\"><pre>PLSRegression(n_components=12)</pre></div> </div></div></div></div></div></div></div></div></div>"
      ],
      "text/plain": [
       "GridSearchCV(cv=KFold(n_splits=5, random_state=0, shuffle=True),\n",
       "             estimator=PLSRegression(),\n",
       "             param_grid={'n_components': range(1, 20)},\n",
       "             scoring='neg_mean_squared_error')"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "param_grid = {'n_components':range(1, 20)}\n",
    "grid = skm.GridSearchCV(pls,\n",
    "                        param_grid,\n",
    "                        cv=kfold,\n",
    "                        scoring='neg_mean_squared_error')\n",
    "grid.fit(X, Y)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1bc745c",
   "metadata": {},
   "source": [
    "As for our other methods, we plot the MSE."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "b702fb04",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-04T23:19:33.611587Z",
     "iopub.status.busy": "2024-06-04T23:19:33.611516Z",
     "iopub.status.idle": "2024-06-04T23:19:33.678469Z",
     "shell.execute_reply": "2024-06-04T23:19:33.678245Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pls_fig, ax = subplots(figsize=(8,8))\n",
    "n_comp = param_grid['n_components']\n",
    "ax.errorbar(n_comp,\n",
    "            -grid.cv_results_['mean_test_score'],\n",
    "            grid.cv_results_['std_test_score'] / np.sqrt(K))\n",
    "ax.set_ylabel('Cross-validated MSE', fontsize=20)\n",
    "ax.set_xlabel('# principal components', fontsize=20)\n",
    "ax.set_xticks(n_comp[::2])\n",
    "ax.set_ylim([50000,250000]);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc9ec466",
   "metadata": {},
   "source": [
    "CV error is minimized at 12,\n",
    "though there is little noticable difference between this point and a much lower number like 2 or 3 components.\n",
    "\n"
   ]
  }
 ],
 "metadata": {
  "jupytext": {
   "cell_metadata_filter": "-all",
   "main_language": "python",
   "notebook_metadata_filter": "-all"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}