Multi Class Logistic Regression with Newtons Method.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multi class logistic regression with newtons method in numpy\n",
    "\n",
    "\n",
    "Softmax regression, also called multinomial logistic regression extends [logistic regression](logistic_regression.ipynb) to multiple classes.\n",
    "\n",
    "**Given:** \n",
    "- dataset $\\{(\\boldsymbol{x}^{(1)}, y^{(1)}), ..., (\\boldsymbol{x}^{(m)}, y^{(m)})\\}$\n",
    "- with $\\boldsymbol{x}^{(i)}$ being a $d-$dimensional vector $\\boldsymbol{x}^{(i)} = (x^{(i)}_1, ..., x^{(i)}_d)$\n",
    "- $y^{(i)}$ being the target variable for $\\boldsymbol{x}^{(i)}$, for example with $K = 3$ classes we might have $y^{(i)} \\in \\{0, 1, 2\\}$\n",
    "\n",
    "A softmax regression model has the following features: \n",
    "- a separate real-valued weight vector $\\boldsymbol{w}= (w^{(1)}, ..., w^{(d)})$ for each class. The weight vectors are typically stored as rows in a weight matrix.\n",
    "- a separate real-valued bias $b$ for each class\n",
    "- the softmax function as an activation function\n",
    "- the cross-entropy loss function\n",
    "\n",
    "The training procedure of a softmax regression model has different steps. In the beginning (step 0) the model parameters are initialized. The other steps (see below) are repeated for a specified number of training iterations or until the parameters have converged.\n",
    "\n",
    "An illustration of the whole procedure is given below.\n",
    "\n",
    "![title](figures/softmax_regression.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* * * \n",
    "**Step 0: ** Initialize the weight matrix and bias values with zeros (or small random values).\n",
    "* * *\n",
    "\n",
    "**Step 1: ** For each class $k$ compute a linear combination of the input features and the weight vector of class $k$, that is, for each training example compute a score for each class. For class $k$ and input vector $\\boldsymbol{x}^{(i)}$ we have:\n",
    "\n",
    "$score_{k}(\\boldsymbol{x}^{(i)}) = \\boldsymbol{w}_{k}^T \\cdot \\boldsymbol{x}^{(i)} + b_{k}$\n",
    "\n",
    "where $\\cdot$ is the dot product and $\\boldsymbol{w}_{(k)}$ the weight vector of class $k$.\n",
    "We can compute the scores for all classes and training examples in parallel, using vectorization and broadcasting:\n",
    "\n",
    "$\\boldsymbol{scores} = \\boldsymbol{X} \\cdot \\boldsymbol{W}^T + \\boldsymbol{b} $\n",
    "\n",
    "where $\\boldsymbol{X}$ is a matrix of shape $(n_{samples}, n_{features})$ that holds all training examples, and $\\boldsymbol{W}$ is a matrix of shape $(n_{classes}, n_{features})$ that holds the weight vector for each class. \n",
    "* * *\n",
    "\n",
    "**Step 2: ** Apply the softmax activation function to transform the scores into probabilities. The probability that an input vector $\\boldsymbol{x}^{(i)}$ belongs to class $k$ is given by\n",
    "\n",
    "$\\hat{p}_k(\\boldsymbol{x}^{(i)}) = \\frac{\\exp(score_{k}(\\boldsymbol{x}^{(i)}))}{\\sum_{j=1}^{K} \\exp(score_{j}(\\boldsymbol{x}^{(i)}))}$\n",
    "\n",
    "Again we can perform this step for all classes and training examples at once using vectorization. The class predicted by the model for $\\boldsymbol{x}^{(i)}$ is then simply the class with the highest probability.\n",
    "* * *\n",
    "\n",
    "** Step 3: ** Compute the cost over the whole training set. We want our model to predict a high probability for the target class and a low probability for the other classes. This can be achieved using the cross entropy loss function: \n",
    "\n",
    "$J(\\boldsymbol{W},b) = - \\frac{1}{m} \\sum_{i=1}^m \\sum_{k=1}^{K} \\Big[ y_k^{(i)} \\log(\\hat{p}_k^{(i)})\\Big]$\n",
    "\n",
    "In this formula, the target labels are *one-hot encoded*. So $y_k^{(i)}$ is $1$ is the target class for $\\boldsymbol{x}^{(i)}$ is k, otherwise $y_k^{(i)}$ is $0$.\n",
    "\n",
    "Note: when there are only two classes, this cost function is equivalent to the cost function of [logistic regression](logistic_regression.ipynb).\n",
    "* * *\n",
    "\n",
    "** Step 4: ** Compute the gradient of the cost function with respect to each weight vector and bias. A detailed explanation of this derivation can be found [here](http://ufldl.stanford.edu/tutorial/supervised/SoftmaxRegression/).\n",
    "\n",
    "The general formula for class $k$ is given by:\n",
    "\n",
    "$ \\nabla_{\\boldsymbol{w}_k} J(\\boldsymbol{W}, b) = \\frac{1}{m}\\sum_{i=1}^m\\boldsymbol{x}^{(i)} \\left[\\hat{p}_k^{(i)}-y_k^{(i)}\\right]$\n",
    "\n",
    "For the biases, the inputs $\\boldsymbol{x}^{(i)}$ will be given 1.\n",
    "* * *\n",
    "\n",
    "** Step 5: ** Update the weights and biases for each class $k$:\n",
    "\n",
    "$\\boldsymbol{w}_k = \\boldsymbol{w}_k - \\eta \\, \\nabla_{\\boldsymbol{w}_k} J$  \n",
    "\n",
    "$b_k = b_k - \\eta \\, \\nabla_{b_k} J$\n",
    "\n",
    "where $\\eta$ is the learning rate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multiclass logistic regression implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "class MultiClassLogisticRegression:\n",
    "        \n",
    "    def fit(self, X, y, epochs=10):\n",
    "        self.classes = np.unique(y)\n",
    "        self.class_labels = {c:i for i,c in enumerate(self.classes)}\n",
    "        y=self.one_hot(y)\n",
    "        self.loss = []\n",
    "        X = np.insert(X, 0, 1, axis=1)\n",
    "        self.weights = np.zeros(shape=(len(self.classes), X.shape[1]))\n",
    "        Xs = X.T.dot(X)\n",
    "        for i in range(epochs):\n",
    "            self.loss.append(self.cross_entropy(y, self.predict_(X)))\n",
    "            h = self.predict_(X)\n",
    "            invH =  np.linalg.pinv(Xs * np.sum(h.T.dot(1-h)))\n",
    "            gradient = (h - y).T.dot(X)\n",
    "            self.weights -= gradient.dot(invH)\n",
    "            print(' Training Accuray at {} iterations is {}'.format(i+1, self.score_(X, y)))\n",
    "        return self\n",
    "    \n",
    "    def predict(self, X):\n",
    "        return self.predict_(np.insert(X, 0, 1, axis=1))\n",
    "    \n",
    "    def predict_(self, X):\n",
    "        pre_vals = np.dot(X, self.weights.T).reshape(-1,len(self.classes))\n",
    "        return self.softmax(pre_vals)\n",
    "    \n",
    "    def softmax(self, z):\n",
    "        return np.exp(z) / np.sum(np.exp(z), axis=1).reshape(-1,1)\n",
    "\n",
    "    def predict_classes(self, X):\n",
    "        return np.argmax(self.predict(X), axis=1)\n",
    "\n",
    "    def one_hot(self, y):\n",
    "        return np.eye(len(self.classes))[y.reshape(-1)]\n",
    "    \n",
    "    def one_hot(self, y):\n",
    "        return np.eye(len(self.classes))[np.vectorize(lambda c: self.class_labels[c])(y).reshape(-1)]\n",
    "    \n",
    "    def score(self, X, y):\n",
    "        return np.mean(self.predict_classes(X) == y)\n",
    "    \n",
    "    def score_(self, X, y):\n",
    "        probs = self.predict_(X)\n",
    "        return np.mean(np.argmax(probs, axis=1) == np.argmax(y, axis=1))\n",
    "    \n",
    "    def cross_entropy(self, y, probs):\n",
    "        return (-1 / len(probs)) * (y * np.log(probs)).sum()\n",
    "    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementation Evaluation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Training Accuray at 1 iterations is 0.94713411241\n",
      " Training Accuray at 2 iterations is 0.94713411241\n",
      " Training Accuray at 3 iterations is 0.94713411241\n",
      " Training Accuray at 4 iterations is 0.94713411241\n",
      " Training Accuray at 5 iterations is 0.94713411241\n",
      " Training Accuray at 6 iterations is 0.94713411241\n",
      " Training Accuray at 7 iterations is 0.94713411241\n",
      " Training Accuray at 8 iterations is 0.94713411241\n",
      " Training Accuray at 9 iterations is 0.94713411241\n",
      " Training Accuray at 10 iterations is 0.94713411241\n",
      "0.9471341124095715\n"
     ]
    },
    {
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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# import some data to play with\n",
    "digits = datasets.load_digits()\n",
    "X = digits.data  # we only take the first two features.\n",
    "Y = digits.target\n",
    "lr = MultiClassLogisticRegression()\n",
    "lr.fit(X,Y)\n",
    "\n",
    "pre = lr.predict_classes(X)\n",
    "print(lr.score(X,Y))\n",
    "\n",
    "fig = plt.figure(figsize=(8,6))\n",
    "plt.plot(np.arange(len(lr.loss)), lr.loss)\n",
    "plt.title(\"Development of loss during training\")\n",
    "plt.xlabel(\"Number of iterations\")\n",
    "plt.ylabel(\"Loss\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Training Accuray at 1 iterations is 0.793333333333\n",
      " Training Accuray at 2 iterations is 0.793333333333\n",
      " Training Accuray at 3 iterations is 0.793333333333\n",
      " Training Accuray at 4 iterations is 0.793333333333\n",
      " Training Accuray at 5 iterations is 0.793333333333\n",
      " Training Accuray at 6 iterations is 0.793333333333\n",
      " Training Accuray at 7 iterations is 0.793333333333\n",
      " Training Accuray at 8 iterations is 0.793333333333\n",
      " Training Accuray at 9 iterations is 0.793333333333\n",
      " Training Accuray at 10 iterations is 0.793333333333\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "0.7933333333333333"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn import datasets\n",
    "\n",
    "# import some data to play with\n",
    "iris = datasets.load_iris()\n",
    "X = iris.data[:, :2]  # we only take the first two features.\n",
    "Y = iris.target\n",
    "\n",
    "logreg = MultiClassLogisticRegression()\n",
    "\n",
    "# Create an instance of Logistic Regression Classifier and fit the data.\n",
    "logreg.fit(X, Y)\n",
    "\n",
    "# Plot the decision boundary. For that, we will assign a color to each\n",
    "# point in the mesh [x_min, x_max]x[y_min, y_max].\n",
    "x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5\n",
    "y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5\n",
    "h = .02  # step size in the mesh\n",
    "xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))\n",
    "Z = logreg.predict_classes(np.c_[xx.ravel(), yy.ravel()])\n",
    "\n",
    "# Put the result into a color plot\n",
    "Z = Z.reshape(xx.shape)\n",
    "plt.figure(1, figsize=(4, 3))\n",
    "plt.pcolormesh(xx, yy, Z, cmap=plt.cm.Paired)\n",
    "\n",
    "# Plot also the training points\n",
    "plt.scatter(X[:, 0], X[:, 1], c=Y, edgecolors='k', cmap=plt.cm.Paired)\n",
    "plt.xlabel('Sepal length')\n",
    "plt.ylabel('Sepal width')\n",
    "\n",
    "plt.xlim(xx.min(), xx.max())\n",
    "plt.ylim(yy.min(), yy.max())\n",
    "plt.xticks(())\n",
    "plt.yticks(())\n",
    "\n",
    "plt.show()\n",
    "logreg.score(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8,6))\n",
    "plt.plot(np.arange(len(logreg.loss)), logreg.loss)\n",
    "plt.title(\"Development of loss during training\")\n",
    "plt.xlabel(\"Number of iterations\")\n",
    "plt.ylabel(\"Loss\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "python3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.16"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}