6. kernelized_svm.ipynb

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   "source": [
    "import pandas as pd \n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt "
   ]
  },
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    "=================================================================================================================\n",
    "# Lecture Notes: Kernelized Support Vector Machines\n",
    "\n",
    "\n",
    "##### D.Vidotto, Data Mining: JBI030 2019/2020\n",
    "\n",
    "\n",
    "================================================================================================================="
   ]
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    "So far, we have dealt with linear models, which work great when the task is to find linear decision boundaries. But what if the data are intrinsically non-linear, and therefore more complex boundaries are needed to separate the classes? In this case (high bias regime), adding new features to the dataset is beneficial. A way to add new features is to use transformations of the original ones, such as interactions and polynomial expansions. This is when kernels, thanks to a technique called the *kernel trick*, come useful to our cause. With this trick, Support Vector Machines can be reformulated so that they can accommodate for different kernels, providing us with a very powerful (but not easily interpretable) tool for predictions. \n",
    "\n",
    "In this notebook, we are going to review the following topics: \n",
    "\n",
    "1. Motivating Examples \n",
    "1. Introduction to Kernels \n",
    "1. Types of Kernels \n",
    "  * Linear kernel \n",
    "  * Polynomial kernel\n",
    "  * Radial Basis Function Kernel \n",
    "1. Kernels in Support Vector Machines \n",
    "  * SVM: Dual problem \n",
    "  * Regularization\n",
    "1. Other remarks \n",
    "1. Examples in Python \n",
    "1. Application to the Heart Dataset "
   ]
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    "## 1. Motivating Examples \n",
    "Consider the following two datasets: \n",
    "\n",
    "<img src=\"./img/kernelized_svm/circles_and_cluster_data.png\" width=\"600\" height=\"50\"/>\n",
    "\n",
    "They appear to be highly non-linearly separated. Indeed, the decision boundaries found by training a linear model (such as a linear SVM model) on such datasets are poor: \n",
    "\n",
    "<img src=\"./img/kernelized_svm/circles_cluster_data_linear_svm.png\" width=\"600\" height=\"50\"/>\n",
    "\n",
    "In Dataset A, about half of the training points from both classes are in both sides of the boundaries; in Dataset B, there is a whole cluster of points belonging to the positive class that are in the side of the hyperplane in theory designated to the negative class. How to solve this situations? \n",
    "\n",
    "Here, linear model suffer from having *high bias*; that is, they cannot capture the exact relationships between the output and the input features. In this cases, one possible solution is to increase the **feature dimensionality** by adding more features to our dataset (*features expnasion*). Such features can be newly measured features, or they can be built starting from existing ones. In particular, interactions and polynomial transformations can often help linear models to find a separating hyperplane. \n",
    "\n",
    "We perform two transformations to the datasets above: in dataset A, we add a feature $x_3 = \\sqrt{x_1^2 + x_2^2}$; for dataset B, we add a feature $x_3 = x_1^2$ (but we could have equally chosen $x_2^2$). These are the resulting datasets, in 3 dimensions: \n",
    "\n",
    "<img src=\"./img/kernelized_svm/circles_cluster_data_expanded.png\" width=\"1200\" height=\"50\"/>\n",
    "\n",
    "It seems now a much easier work for our linear SVM model to find a separating hyperplane! Let's re-train it, on the new 3-dimensional datasets and plot the separating hyperplanes: \n",
    "\n",
    "<img src=\"./img/kernelized_svm/circles_cluster_data_svm_3d.png\" width=\"1200\" height=\"50\"/>\n",
    "\n",
    "The decision boundaries are much more sensible now. We can project the resulting decision boundary back to the original 2-dimensional space, obtaining the decision boundaries we would initially expect: \n",
    "\n",
    "<img src=\"./img/kernelized_svm/3d_svm_in_2d.png\" width=\"600\" height=\"50\"/>\n",
    "\n",
    "In higher dimensions (large $p$), it is often difficult, if not infeasible, to calculate by hand and add to the dataset all the possible powers and combinations of features. Fortunately, there is a mathematical tool that can help us to perform exactly this operation while sparing us with all the computations: such tools are the **kernels**.   \n",
    "\n",
    "\n",
    "## 2. Introduction to Kernels \n",
    "Ideally, we would like to obtain all possible interactions and polynomial terms (up to a degree $d$) by means of a transformation $\\phi$, to be apply to each vector of observations $\\mathbf{x}_i$. For example, a *quadratic* feature map takes all polynomial and interactions up to degree 2:  \n",
    "\n",
    "$$\\mathbf{x} = \\begin{bmatrix} x_1 \\\\  ... \\\\ x_p\\end{bmatrix} \\stackrel{\\phi}{\\longmapsto} \\phi(\\mathbf{x}) = \n",
    "\\begin{bmatrix} x_1 \\\\ ... \\\\ x_p \\\\ x_1^2 \\\\ ... \\\\ x_p^2 \\\\ \\sqrt{2}x_1x2 \\\\ ... \\\\ \\sqrt{2}x_{p-1}x_p \\end{bmatrix}$$\n",
    "\n",
    "While such expansions allows for flexible decision boundaries, the new number of dimensions (and therefore of our new dataset) explodes quickly as $p$ increases, making the ensuing algorithms exceptionally slow.\n",
    "\n",
    "Fortunately, there is a mathematical tool that allows us to expand the dataset without having to explicitely specify all the new $2^p$ features: kernels.\n",
    "\n",
    "**Kernels**. [*Kernels*](https://en.wikipedia.org/wiki/Kernel_method) can be seen as special functions that calculate the inner product between two vectors (which is a way to measure their similarity, or distance). Formally, a kernel function for two vectors $\\mathbf{x}$ and $\\mathbf{z}$ is defined as the inner product of the transformations of such vectors: \n",
    "\n",
    "$$K(\\mathbf{x}, \\mathbf{z}) = \\phi(\\mathbf{x})^T\\phi(\\mathbf{z})$$\n",
    "\n",
    "Notice that the function maps two elements in the vector space $\\mathbb{R}^{p\\times p}$ to a real scalar, so that $k(\\cdot,\\cdot) \\in \\mathbb{R}$.\n",
    "\n",
    "Kernels make it possible to calculate the inner product of two mapped vectors directly from their original space, rather than in the expanded space (that is, with no need to compute the $\\phi$ transformations). In this way, we can perform $\\mathcal{O}(p)$ instead of $\\mathcal{O}(p^2)$ computations. For two vectors of data points $\\mathbf{x}_i$ and $\\mathbf{x}_j$, the quadratic kernel becomes: \n",
    "\n",
    "$$K(\\mathbf{x}_i, \\mathbf{x}_j) = \\phi(\\mathbf{x}_i)^T\\phi(\\mathbf{x}_j) = \\mathbf{x}_i^T\\mathbf{x}_j + (\\mathbf{x}_i^T\\mathbf{x}_j)^2$$\n",
    "\n",
    "**Example with p=2, d=2**. Let's see an example with 2 two-dimensional vectors, $\\mathbf{v}$ and $\\mathbf{z}$, defined as: \n",
    "\n",
    "<br>\n",
    "$$\\mathbf{v} = \\begin{bmatrix} 3 \\\\ 5 \\end{bmatrix}$$\n",
    "<br>\n",
    "\n",
    "<br>\n",
    "$$\\mathbf{z} = \\begin{bmatrix} 1 \\\\ 2 \\end{bmatrix}$$\n",
    "<br>\n",
    "\n",
    "\n",
    "Their *quadratic feature maps* are: \n",
    "\n",
    "<br>\n",
    "$$\\phi(\\mathbf{v}) = \\begin{bmatrix} 3 \\\\ 5 \\\\ 9 \\\\ 25 \\\\ \\sqrt{2}\\cdot 15 \\end{bmatrix} $$\n",
    "<br>\n",
    "\n",
    "<br>\n",
    "$$ \\phi(\\mathbf{z}) = \\begin{bmatrix} 1 \\\\ 2 \\\\ 1 \\\\ 4 \\\\ \\sqrt{2}\\cdot 2 \\end{bmatrix}$$\n",
    "<br>\n",
    "\n",
    "The inner product of such transformations is: \n",
    "\n",
    "$$\\phi(\\mathbf{v})^T\\phi(\\mathbf{z}) = 3\\cdot1 + 5\\cdot2 + 9\\cdot1 + 25\\cdot 4 + 2\\cdot15\\cdot2 = 182$$\n",
    "\n",
    "Let's now try to perform the same computation with the kernel: \n",
    "\n",
    "$$K(\\mathbf{v}, \\mathbf{z}) = \\mathbf{v}^T\\mathbf{z} + (\\mathbf{v}^T\\mathbf{z})^2 = 3+10 + (3+10)^2 = 182 $$\n",
    "\n",
    "It works! We obtained the same results, without having to perform the quadratic transformation via $\\phi$. \n",
    "\n",
    "But there's more: the quadratic mapping is only an example of the possibile transformations that we can implicitly apply with kernels (for example, it is possible to increase the polynomoial degree to obtain even more flexibility), as we will see shortly. \n",
    "\n",
    "**Kernel Matrices**. Kernels allow to infer all possible cross-correlations between the features by calculating the inner products between vectors of data points. In this sense, kernels can be seen as a measure of 'similarity' (or distance, depending on the type of kernel) between two observations. For a training dataset of $n$ observations, kernels are calculated for each pair of units. This leads to the $n \\times n$ Kernel Matrix $\\mathbf{K}$, whose elements in the $i$-th row and $j$-th column is: \n",
    "\n",
    "$$K_{ij} = \\phi(\\mathbf{x}_i)^T\\phi(\\mathbf{x}_j)$$\n",
    "\n",
    "and therefore $\\mathbf{K}$ is defined as: \n",
    "\n",
    "$$\\mathbf{K} = \\begin{vmatrix} K_{11}& \\cdots & K_{1n} \\\\ \\vdots & \\ddots & \\vdots \\\\ K_{n1} & \\cdots & K_{nn} \\end{vmatrix}$$\n",
    "\n",
    "This matrix therefore defines the new *feature matrix*, and is $n \\times n$ indipendently on the number of original features $p$. Therefore, the computational costs of the alogrithm now depend on the number of data points only, rather than also the number of features. \n",
    "\n",
    "Kernel matrices have the following properties: (a) they are *symmetric*; (b) they are *positive semi-definite* (which means that none of its eigenvalues can be smaller than 0). Therefore, not all functions can be used as kernels, but only those that lead to a kernel matrix having properties (a) and (b). \n",
    "\n",
    "We are now going to explore some of the most common kernels used in Data Mining and Machine Learning. After that, we will see how to apply them to the SVM algorithm. \n",
    "\n",
    "### 3. Types of Kernels \n",
    "\n",
    "**Linear Kernel**. The *linear kernel* is simply the inner product of two vectors, $\\mathbf{x}$ and $\\mathbf{z}$. It is therefore defined as: \n",
    "\n",
    "$$K(\\mathbf{x},\\mathbf{z}) = \\mathbf{x}^T\\mathbf{z}$$\n",
    "\n",
    "This is simply an identity mapping to the original feature space; standard linear models, such as Linear SVM, implicitly use a linear kernel. \n",
    "\n",
    "**Polynomial Kernel**. As mentioned in the previous section, it is possible to generalize quadratic mappings of the features up to a desired degree of polynomial powers and interactions. This is possible with the polynomial kernel: \n",
    "\n",
    "$$K(\\mathbf{x},\\mathbf{z}) = (\\mathbf{x}^T\\mathbf{z} + r)^d$$ \n",
    "\n",
    "where: \n",
    "* $r$ (often set to 0 or 1) controls how much the kernel is influenced by higher degrees polynomials\n",
    "* $d$ is the desired degree of the polynomial \n",
    "\n",
    "Thus, the polynomial kernel allows expanding the feature space up to a polynomial degree $d$, implying an intrinsic dimensionality of $p+d\\choose{d}$ in the new kernel space.  In this case, kernels measure \"similarity\" between data points.   \n",
    "\n",
    "**Radial Basis Function Kernel** (a.k.a. Gaussian kernel). The Radial Basis Function (or RBF) kernel is:\n",
    "\n",
    "$$K(\\mathbf{x},\\mathbf{z}) = \\exp{(-\\gamma ||\\mathbf{x}-\\mathbf{z}||^2)}$$\n",
    "\n",
    "The RBF kernel is also called Gaussian Kernel, as its function corresponds to the exponential part of the Gaussian density. In this respect, $\\gamma \\geq 0$ can be seen as the parameter that controls the width of the kernel. \n",
    "\n",
    "In practice, RBF kernels try to place a non-normalized (multivariate) Gaussian distribution upon each training point (which then become the means of the Gaussians), and calculate the \"distance\" between each mean and the other data points. In this graph, we can see how the RBF kernel is placed upon a unit $\\mathbf{x}_i$ in one dimension (generalization to $p>1$ dimensions is straightforward): \n",
    "\n",
    "<img src=\"./img/kernelized_svm/rbf_xi.png\" width=\"500\" height=\"50\"/>\n",
    "\n",
    "And here we can see how two observations, $\\mathbf{x}_i$ and $\\mathbf{x}_j$ are compared in one dimension (in this case $\\gamma=70$): \n",
    "\n",
    "<img src=\"./img/kernelized_svm/rbf_kernel.png\" width=\"650\" height=\"50\"/>\n",
    "\n",
    "Last, let's see the effect of modifying $\\gamma$ on the shape of the RBF Kernel: \n",
    "\n",
    "\n",
    "<img src=\"./img/kernelized_svm/rbf_varying_gamma.png\" width=\"500\" height=\"50\"/>\n",
    "\n",
    "From a theoretical perspective, the RBF kernel implicitly works as polynomial kernel of degree $+\\infty$ which makes it a very powerful and popular kernel. \n",
    "\n",
    "## 4. Kernels in Support Vector Machines \n",
    "SVM in combination with kernels result in a very powerful and flexible prediction algorithm. In order to understand how to include kernel functions in SVM, we first need to understand its dual optimization problem.\n",
    "\n",
    "### 4.1 SVM: Dual Problem\n",
    "You should recall from the past lecture the optimization problem for linear SVM (where $y_i \\in \\{-1,1\\}$): \n",
    "\n",
    "$$\\min_{w_0,\\mathbf{w}}\\mathbf{w}^T\\mathbf{w} + C\\sum_{i=1}^n\\xi_i$$\n",
    "$$\\ s.t.\\\n",
    "\\left\\{\n",
    "\\begin{array}{l}\n",
    "y_i(w_0+\\mathbf{w}^T\\mathbf{x}_i) \\geq 1-\\xi_i\\ \\forall i \\\\\n",
    "\\xi_i \\geq 0\\ \\forall i\n",
    "\\end{array}\n",
    "\\right. \n",
    "$$\n",
    "\n",
    "This is also known as the *primal* problem of SVM. As the problem is convex, it turns out that it is possible to write this problem with its [*dual*](https://en.wikipedia.org/wiki/Duality_(optimization)) formulation, which is formally different but leads to the same solution. This is because in SVM they satisfy the [Karush-Kuhn-Tucker (KKT)](https://en.wikipedia.org/wiki/Karush%E2%80%93Kuhn%E2%80%93Tucker_conditions) conditions. \n",
    "\n",
    "The dual optimization problem is: \n",
    "\n",
    "$$\\min_{\\alpha_1,...,\\alpha_n} \\sum_{i=1}^{n}\\alpha_i + \\frac{1}{2}\\sum_{i=1}^{n}\\sum_{j=1}^{n}\\alpha_i\\alpha_j y_iy_j \\mathbf{x}_i^T\\mathbf{x}_j$$\n",
    "$$\\ s.t.\\\n",
    "\\left\\{\n",
    "\\begin{array}{l}\n",
    "0 \\leq \\alpha_i \\leq C\\ \\forall i \\\\\n",
    "\\sum_{i=1}^{n} y_i\\alpha_i = 0 \n",
    "\\end{array}\n",
    "\\right. \n",
    "$$\n",
    "\n",
    "Here, the solution for $\\mathbf{w}$ is $\\mathbf{w} = \\sum_{i=1}^{n} \\alpha_i y_i \\mathbf{x}_i$. There is a nice interpretation of the $\\alpha_i$'s in the dual problem: they are larger than $0$ only for those units that are support vectors (that is, that lie on the margins or inside it, or that are in the wrong side of the hyperplane), while for all other units they are equal than 0. \n",
    "\n",
    "The decision function $f(\\mathbf{x})$ is now defined as: \n",
    "\n",
    "$$f(\\mathbf{x}) = w_0+\\mathbf{w}^T\\mathbf{x} = w_0 + \\sum_{i=1}^{n} \\alpha_i y_i \\mathbf{x}_i^T\\mathbf{x} $$\n",
    "\n",
    "that, as in the primal problem, classifies units in the positive class if $f(\\mathbf{x}) \\geq 0$, and to the negative class otherwise. You can find more information about the mathematical formulation of SVM in the [scikit-learn documentation](https://scikit-learn.org/stable/modules/svm.html#mathematical-formulation). Algorithms such as the [Sequantial Minimal Optimization (SMO)](https://en.wikipedia.org/wiki/Sequential_minimal_optimization) (and implemented by *libsvm*, which is the optimizer used by scikit-learn) can be used to find the solution to the dual problem of SVM.  \n",
    "\n",
    "\n",
    "**Kernelized SVM**. You may have noticed the dot product present both in the minimization problem, and in the decision function. This means that we can rewrite the problems in terms of kernels: \n",
    "\n",
    "$$\\min_{\\alpha_1,...,\\alpha_n} \\sum_{i=1}^{n}\\alpha_i + \\frac{1}{2}\\sum_{i=1}^{n}\\sum_{j=1}^{n}\\alpha_i\\alpha_j y_iy_j K_{ij}$$\n",
    "$$\\ s.t.\\\n",
    "\\left\\{\n",
    "\\begin{array}{l}\n",
    "0 \\leq \\alpha_i \\leq C\\ \\forall i \\\\\n",
    "\\sum_{i=1}^{n} y_i\\alpha_i = 0 \n",
    "\\end{array}\n",
    "\\right. \n",
    "$$\n",
    "\n",
    "and the decision function becomes: \n",
    "$$f(\\mathbf{x}) = w_0 + \\sum_{i=1}^{n} \\alpha_i y_i K(\\mathbf{x}_i, \\mathbf{x}). $$\n",
    "\n",
    "This reformulation of linear models in terms of kernel functions is known as the **kernel trick**. The kernel matrix of the training dataset can be used for model training, and the kernel function (which, once again, is a way to measure similarity or distance) between all the support vectors found during the training stage and a data point $\\mathbf{x}$ for prediction. (Question: why only the support vectors and not the whole training dataset?) \n",
    "\n",
    "Thus, by substituting the linear kernel (which is equivalent to the original linear formulation of SVM) with the polynomial or RBF kernels with the kernel trick, we can obtain a much more flexible predicting tool, which allows finding complex decision boundaries as the ones seen in Section 1. Of course, both these kernels have their own set of hyperparameters (introduced above), allowing for different levels of model complexity. We are now going to see what is the effect of modifying such hyperparameters.\n",
    "\n",
    "\n",
    "\n",
    "### 4.2 Regularization \n",
    "Modifying the hyperparameter $C$ has the same effect seen for linear SVM; it represents, then, the cost we are willing to pay for miss-classified examples. Therefore, lower values of $C$ allow for more miss-classifications of the training points (larger margins), and vice versa for larger values of $C$. \n",
    "\n",
    "Let's now explore the kernel-specific hyperparameters. Importantly, they tend to be strongly affected by the value of $C$. More in general, SVM's are very sensitive to the choice of the hyperparameters, and so they must be tuned carefully. \n",
    "\n",
    "\n",
    "**Polynomial Kernel**. The polynomial kernel is composed of two hyperparameters, $r$ and $d$ (see above). Typical choices for $r$ are 0 and 1, although this parameter can be tuned. The polynomial degree, instead, is an integer which should always be tuned. When, among a grid of values, the best performing value for $d$ is 1, this may suggest that relationships in the data are linear (notice that $r=0$ and $d=1$ recover exactly the linear kernel). When the best $d$ is 2, this could mean that quadratic relationships are present in the data, and so on. \n",
    "\n",
    "We can see the effect of modifying the degree $d$ and the hyperparameter $C$ in the graph below (we use the dataset of Example B above). \n",
    "\n",
    "\n",
    "<img src=\"./img/kernelized_svm/poly_regularization.png\" width=\"700\" height=\"50\"/>\n",
    "\n",
    "When $d=1$ we find linear relationships in the data, and this models is clearly underfitting (as we have already seen in Section 1 of this notebook). As we increase the polynomial degree, the model captures more nonlinearities, and it might become overfitting for a too large $d$. The best fitting model seems to be reached with $d=2$, suggesting quadratic relationships in this dataset. For low values of $d$, the parameter $C$ doesn't seem to have a too strong effect on the predictions on these data. \n",
    "\n",
    "\n",
    "**RBF Kernel**. The main hyperparameter of the RBF kernel is $\\gamma$ that, as seen above, controls for the width of the Gaussian function placed upon each observation. For large values of $\\gamma$, the Gaussian becomes narrow; as a consequence, the boundaries will focus more on each single point, becoming more complex. For low $\\gamma$, the Gaussian is wider, and the decision boundaries will become smoother (simpler models). \n",
    "\n",
    "Let's now see the effect of modifying $\\gamma$ and $C$ graphically, as done above for the polynomial kernel.\n",
    "\n",
    "<img src=\"./img/kernelized_svm/rbf_regularization.png\" width=\"700\" height=\"50\"/>\n",
    "\n",
    "In this case, the value of $\\gamma=0.01$ seems to lead to the best fitting model, but also values of $\\gamma=0.001$ with $C=10$ seems acceptable. Notice how the boundaries become more complex (dataset-specific) as we increase $\\gamma$, and how the parameter $C$ affects the boundaries (especially when switching from $C=0.1$ to $C=0.5$, for this dataset). \n",
    "\n",
    "\n",
    "\n",
    "## 5. Other Remarks\n",
    "* Kernelized SVM works very well on a large variety of dataset\n",
    "* it is important to scale the features (either with standardization or with normalization) before training kernel SVM's, otherwise the kernel function will tend to base the similarity solely on variables measured on larger orders of magnitude\n",
    "* like linear SVM, they don't have a probabilistic interpretation\n",
    "* unlike linear SVM, it is not possible to consider the weights of the model for variable importance, as the data are transformed by kernels to a different space (in fact, scikit-learn doesn't return a `coef_` array with non-linear kernels)\n",
    "*  Because of the kernel matrices (and the computational demand of the dual problem), kernel SVM's scale well with the number of features, but not with the number of examples in the dataset. For how it is implemented in \"libsvm\", the computational cost of estimating kernel SVM algorithms can reach $\\mathbf{O}(n^3p)$ - against $\\mathbf{O}(np)$ of linear (primal problem) SVM's. Therefore, kernelized SVM is most suited for small or medium-sized training datasets\n",
    "* read more about SVM's on the [scikit-learn](https://scikit-learn.org/stable/modules/svm.html#) page\n",
    "* a popular regression (and probabilistic) version of kernelized models are Gaussian processes; they won't be covered here, but you can find out more about them in the [scikit-learn documentation](https://scikit-learn.org/stable/modules/gaussian_process.html)"
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    "## 6. Examples in Python \n",
    "We are  now going to see an example on the implementation of a kernelized SVM in Python. The `SVC` function, ins the `sklearn.svm` module, allows specifying various hyperparameters: \n",
    "* `kernel`, which can take on values such as `poly` (for the polynomial kernel), `rbf` (for the RBF kernel), and `linear` (for the linear kernel) - the default is `rbf` \n",
    "* `degree`, which specifies the degree of the polynomial kernel \n",
    "* `gamma`, which specifies the value of $\\gamma$ for the RBF kernel \n",
    "\n",
    "You can find out more options for this function in the [documentation](https://scikit-learn.org/stable/modules/generated/sklearn.svm.SVC.html)."
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    "### 6.1: Binary Case \n",
    "In this first example, we will try the \"circles\" dataset (Example A of Section 1 above) with a RBF kernel, and $\\gamma=0.5, C=0.5$. Data will be standardized first. "
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v1JZlZjKxQV6NplsxJANdpkNfbeGplZtlZPQfiU9JFyGtEZsWqU+ZSosi3YJcT1OnM7GBzpj6tHBy3kvNGkbqqjmiEvC8CVQqIMvI8DFvi5DWiC0faZBxiDxzPG2ZkSq7MtjsHaAryqZdnMrWnjpmX02E1klBhLRmdPvNZRFapmPmfIFxcUMmD9ukdsp7YbovyLS/bdnaM68y63Zra+a4NA5ctN5ESFMIrZnspK+2iw7qwJHma1pH9f5+XQvOJM1pJXNwMHuyAp1noFPidVVhfFw/wGWj9jR1r1Rspbooh64EWoQ0QYjNZOsWqe0O6ir/hWp6/yI3lJdmV10kdNNaZMRWljvD1dT0Np+Nh7hqvYmQJgixmWxd/G0+hDwBS5t/s8gN5aXZVRcJW80B02ee1WXKxIQz7YIWePcRVyNtRUgThDqk2WozyOZDMBGwMmPf89Jct0Va9DllBZrKzLifdr748/ZpRhCLiEVakZCGaJFap0qL1NaDVl2nHzDpi1L8uzwfqQ62mgNZzynLP2syzNSEEH1cGoiPtCIhLfKgddxfIQWvSue2+A2rgkqqrczUejrBpOQkBjZejq1zZFmYecvF5lm0RdIYXMbVQ6L2FQgps9mDztMc0xiCNxTNbSpB6zcV48sJ2zb9Q2+emvor4xVCViuiodalT3gppADOB/AkgO0Arkv5/jIAewBs7m1X6pzXRT/SvFaw6nuihuZjkyi268IdmsO7SBS9/9yy1i8Wf5VzvBNSAB0AOwAsBTAEYAuAUxLHXAbgJtNzuxDSvLKaN7FQ8BQdxZP2W9s1S2gCYupPVlmmyeeZlwkbWaNXi0pIB1AfKwFsZ+adzPxbAH8LYHWN6clkZCR7v+p7AHj6afvpqZTJSWDtWmB6OiqW09MAUfqxaQ9ibAzYtQuYmYn+jo3ZTd/69cDw8Ox9w8PRfh8pkyGmp6O/ac8zKxNOT0fvcHKy+LUFJXUK6WIAz8Q+7+7tS/IeInqEiO4kohNVJyOitUQ0RURTe/bssZ3W3LK6fr2ZtnjJ5CSwZAkwMBD97Re6deuA/ftnH8s894brEq+xMWDDBmB0NErT6Gj02bZg26JshlAJYlomjbN/f/QuBfukmalVbAAuAvCl2Of3ItGMB9AF8Ire/x8A8B2dc7saa5/XQk0b+RfMDPhZvkybEyL3r9XAKLE2qmdt2sRXndvU9SJoAw99pGcBuDf2+XoA12cc3wGwT+fcdU5aEs/HReYLro0sP6OJD7JIbeP1g3FE2nMy8Z3mCWKR/qpCLj4K6TwAOwGchCPBpmWJYxbF/r8QwAM65/Zh9qfQ4h+Z0TTdyHvecePj2YW77ZhE8/OeV9652lh5WcA7IY3ShFUAtiGK3q/r7fsYgD/s/f9xAI/1RPa7AN6gc14fhDS0HjmZY7p1O7Tn9XHMchF4+2AqJqtJYyqCeVauVF7GqISUou+axYoVK3hqaqrWNCxZciTAGmd0NAq0ekc/Mp8MKgFRAEMneDMwEBXRInj7YGpClYE6HeD2280Caar3QhRF/gVtiGgTM69I7q8zat9oQuuRczjy3enM/U432ls0Gk3k8YOpCVUXqZkZ894IeX33AkfV2aRS0szU0DcbTXtfhmY7w7RTt07TOy2QpLOVHUfr9YMuiE0ne4OHjlZ9a/DRR+pqKyukDc53EVk3WLQAFxn2aGMygqa+LJsTyoyORs+5aZUNVx/UFSE1ILiIuylFJr7IK4hFptGzUZib/LLSLG0d67uplUsKVQd1RUgNCC7iborpVGxZE2XknTO5tX3CkjLoCmTWnK0NQyxSj4W0yUYOM5vfoM7xWYVXJiyxg+692lws3nP/s/hIPRbSxreMTG9Qx+qr66E1/mXF0LW+s+Y6NalgAnm2VWq9CGkKWS/A84q4PCY3qDvcsK6H1viX1UPXIi2z1HWR67UIEdIEJqMe21BG5xC/8QUL1AXTUyulkehmWluT43rmf/ahLIqQJtCpbANp2dinSFemFlsplVJmqK7pcg0eWaS+lEUR0gQ6la1H+ahaiszg3sQoeaikqU6RPrsezdTlS1lUCWlrh4jqjJpTjdILfsb7PIrcYEOGGzaCtImuv/pV4AtfiL7vj6kkAubNi/4mx1ZOTkZj+pmP7CMC1qypZMLs5LDPtGkHgGh/bcNC46Spa+ibLR+pbi3og+/GKqYWaSv8HQ0hy20Tf481moAqg9qHLAhp2s8lTwCzxDbYCZx1mJiIllZW5drk2usNHX7YSPIqyb5Q1hhoynLxZiXddZdlZhHSwqQN8tFZkjxoP+rEBPPQkPrGkv3EfIgCCHrkqVFfKGu0SPM6HdTZUBIhtYBJMDu42Eu8xuh0skU0XrOoapWga5IGo2uR1lhB5mm4iZjazoYipCXIm2g8eB3JskDTqvlG1iQtQddH2j+2BpdNnobXadCIkBakSJfK4Fq2Or4K0y2omqRlxC2DfuvDM9+2TvyijoaRSkhlqZEcsrpexCGKXt3oaDTZu69LqqeSXJ++LLpLkwiCJdJWynGRDWWpkYLodKnsdqNueszRskON1Y8BjewyOioi6hpba2t4sUaHHdK6zlaaDdPM1NA3m0173fk6vEXHz6XTtB8aYh4YyD5G/KLusTVJhPS2KASK+EgBHAPg5JT9b876Xd2bax9pMPnNpNAl+40ODMzuK9r4Pl+BoFOz2xxtEhiu42PGQgrgEgA/AbAZ0dryZ8S+e1j1O5MNwPkAngSwHcB1Kd+/AsDXet//EMASnfO6itoH19/cpLDkLWvRuAhboOgM8dGJvHg2s5MNqjB6igjpZgCLev+vBPAjABf2Pv8/1e90NwAdADsALAUwBGALgFMSx1wN4Jbe/5cC+JrOuV31Iw2OMoXFpLtCULVL4BSZUCbtvTfQIq3illRCmhU96DDzcz0/6oMA/j2A/05Efw6Azb2xc1gJYDsz72Tm3wL4WwCrE8esBnB77/87AZxLZDvE3GDKrGe+bt3sEGgaw8PAxETDI2yesX599NyL0H/vk5PAr3899/vh4ej8gVLnJENZQvoCEZ3c/9AT1XMQidsyC9deDOCZ2OfdvX2pxzDzQQD7AHQtXNsIneCmlwHQtEKnKiy60+0ANYVFBQCzw9MqhobU773fT2jv3tnfd7vBv88ydkNp0szUyILFcgCvw9zm9iCA96p+p7sBuAjAl2Kf3wvgpsQxjwI4IfZ5B4CFivOtBTAFYGpkZMSaKa/jd/E6IKXj4DWZbifgpl/jyAoA9ieSAWZ3um/wkF4vfaSHD4jE7C8AEIBXAvgcgB/k/U7jvGcBuDf2+XoA1yeOuRfAWb3/5wF4HogGEWRtVXR/iue74N1NutPteFM7CMycP7tHoyeHSKeuqL1Oh/zfA3AigO8DeAhRJP8PDA3fNB4C8DoiOomIhhAFk+5KHHMXgDW9/y8C8J3ezVSGjt8l6AmgJyfVzXjmGns4C6nEXTBZAySeflrPz93nuOOsJK9uxsYil/3MTLWu+3kaxxwA8BIia3Q+gKeYeabshZn5IBFdg8jq7AC4lZkfI6KPIVL9uwD8DYCvEtF2AL9AJLaVMjKSrjNxv4vOMV7S95epGB2NcqPgB8lxkIcOqY8dGQmkJm8IaWZqfEPULeljiHyjiwD8A4Cv5/2uzq3KDvkTE+mLbAbRCs7qShPEDbQM3a5P/Xdn0lWqIU1716BE0/4KZv5LZj7AzM8x82rMbYI3lqwxvJOTwOWXAy++OPd3FS1tU44siyWvGe9lN4WGk/W+khkUSO/ipOo96H3zyXPS1DX0zWWHfJ35j4EoOOo9RRelGh/3uJtCgzF5X2lBpm6X+dxzWxtEtBGIgsxHWh7TuUm9p2jfLt2uUcGOrfUU3f49KsHtdu0s0xwgtrpGiZBawHR0XhDkiV1RP5vXnWsDRqdy0pkbIasCDADTOtpWF0URUguY5E+Tpr3XhpvJTTeqc23AmNb4gQWaitTRtuZoUQmpTOxsgKk/Xif+0u/RMj0dvdrp6ehzrbEbnb6KyaBFcuhp0J1rA0c1NLirGF0dWKAprXvs/v3RfhXOh4+mqWvoW5U+0uFh9RLNOi1Z7ww3HUdw/6aLuATEIq0G1bSIDXC3FLEuxUfqkZAyq5vhRXXDOx+r6kY6HTPfQ1bkOLCC6zWmfiGv/Uh6FC1rErX3SEhVFPXBqLpQdTrVpHsOeeO3TcW0qKkuzEW6oTFzvYa1CGkGNmqqxlukRfseShPfDmnLwWRVeA1HVWa9W2ok5M1ESG3VbkXP453OmM6Mn0cDl7SoBZ01s1r+bL2eRi/EzURIbQpZkdrQS/9/fJx2VlNfp8B6V1MEiq6Ixp9tA/yhJtS51EjtoudiMxFSHwwmb/O7Tn/EvAR7WVMEiIk1Oj6e/twHB2evDNuwd1BFWRYhVSAGUwa6nfHzhNHbmiIgVE37+fPT/dc6roCGVWi+Ln7XCnSWNWrtREe6vZXzekPXNdtuk7jxxmgtpjhDQ8CCBZFexNm/f+6aTGnkvbfAyCrLzstwmrqGvtmM2re6ZWo6S4tYm25Jy6im4+rr9GFVgOtxCJCmfTFa3/RP5sy0WaxbWctYpqj7w2Smp5Zl5Ly5rYvcughpQXwIRnmByYzrDS6cTihjMmX9Ni7O3S7z0FBrKj2dxlSRMqwS0tb7SPOoda1sX4jPrKKDTExiRpFZOPpkLeEQ56ijgCuuaM1ihjrr/lktw2nqGvpW5ZpNrcB0WjYTi1Qi+m6aPS3PuHmuY/GRViykzFLWjQIaJjm05YX9MKaOeJ0M2XLnfp5vtGgWEyEVipNnkQ4MFKtlWl7YD2NSoege23Lnvqs6WoRUKM7ERLaQFs2dVRZ235sVuunTrXykknLyyr0SUgDHAfg2gB/3/h6rOO4QgM297S7d84uQlkCV+1QjZcosl6pb2MuWiCbNjapb+YjbxAm+CeknAVzX+/86AJ9QHPfrIucXIS1IXlearBUobc7YEp99/6ij5oqGqSBkuSZciItL61dVoaVZmr5b4QHim5A+CWBR7/9FAJ5UHCdCWiV5FuL4ePq47jITDOtMVly2iZoXLLPZ3HVpCU5MzO0LCkSTkYhIVoJvQvpvsf8p/jlx3EEAUwAeAPBu3fMXFdLWV+B5zUbdSZ/LNPt1u1qZ+FHzzmnTJ+vSN5k1iilQdMpc3hDuKsts5UIK4D4Aj6Zsq5PCCeCXinMs7v1dCmAXgJMzrre2J7pTIyMjxg9IXEqcLwJFxnWbPkDda5iud51l5dq0SF0G0BoWidcpc6beJtdl1jeLVKtpn/jNbQAu0jl/EYtUgpycn2tVC0zZbDbrWqRDQ2YlZmKimvWjXM4UbuIfDQCdR6U6JisrunwcvgnppxLBpk+mHHMsgFf0/l/Yi/CfonP+IkLasMq+OLrT5+hupg/Q5FpFZoJ33Ra0ZSapJmZu0Hh5nTJXpBHkssz6JqRdAPf3xPE+AMf19q8A8KXe/78PYCuALb2/V+ieXyxSy+hYiQMD9h5gcrKNrBLjo0+mrOOPOdsf2hBHfhmLVKd+dYFXQup6KyKkPpZHb9AZuOxyaeCsEudTDahr7epkNpP+okWE1YPIalEfaV5WbI2P1PXmKmrvQd6rB92By6oH5KJDfb/E+OKTMamJy5hi8WOK1v4eWQ2mxnueb7RxUfs6Nxf9SMvmvaBFuMzN2/QZpj1AXyxSk3ToiL/Ocyt67748swLUXQeIkJakTN6r++VboWhNUPTB2WwmV4GJZaxrbcb9w/3z9wctZLUS8qxxX6z4gtRplIiQlqRM3gvYAChPkQen6zyLB6TqXmbY5CXn3V+ZXhINtkh9aNWJkJakTBA1SAPAVq7N6ghoGrGOd3cymXYubtm5mqjE1DLOer5FQtUm1rgvVrwBviRZhLQkaS9yaCjq2pf3coMzAGzmWh3ryjRirTtUcmLC3dh0VX9bG5VP0ZVB+5EYnWv7YN4ZkFWGqrwVEVILFB1o4kttqo1t5dcJu5pErLOERteyK1OL2X6hyYyVt1KrztawiUyyXrnpqygjvCKkDjBpsgdlANQ9XjxPqHQFMqv0lbkXXT9PfDrArL49ZfyhWVvAk5kkyfIQmdSTZetAEVIHBNdk18XljemeO6vmmZjQE0hXFvBIx4IAABegSURBVGnRpreJ3ycr3UmBzjq+IagE0PTWy2ZtEVIHuG6y12bFuuz7qZrTNK8ndvIBpE34nCwRWT7S8fHZvpn+EFedB501bFVHCOP3ZfrbNFogpMzp2UEljP3Rw0nKNrZESB3hSuxq96u6GI2UFp2Lz7Kf9/v4TFTJ8/TPn0xnWtR+fDxdYONbVnS/jJDqmFKq35imp0FNexUTE2pxTKt3xCL1VEhdEbzbwKTJaprjdaP2ZdOmEq+iTXug+FSEedGTZMVgOs1gwKgemypWIT5Sza0JQhpk39M4pmKTzMlZD0A3am8jbSYirzO5i6mI6r7woKKZsymbdFOjQ6L2LRLSVlmkaWZBEYtU17wwTVsSlVmTDAKlRe2LBJcCJy9uWNaFVaUbTIQ0AJKjHnU6+3uLro9UJRp5PtIyS4eoglAqi9A0EGb6XLKs72BeeDpFe7KZ1h9VGeQipJ6j0p26h5CXQjX6R7cZa6MLVFba0iYFqcIqTN5X2lyuqiBcYBQdW+GrC0uEtEKK1I66fbyDE9M0bJkhtv0feU1sly8hYB9nFkVH+/rq0RAhrYii/hrd+EdQzXsVNvup2nSO6QaRGvESqiFPKGvv5meICGlFFK1hy/YWCg4TCyyviW/LkjPxXzbiJbhHRyirer02ECGtiKI+H5Mh1776j5xQhcmSjPLFHdPyEkpjMy5Xt7UqQloRZXw+yQzXsGXMi+E6rFtFWNk3syoQfPSfipBWhM1a1McauXJshHWz+n3mTR9U9iXISyyMjxF9EdIKse22a7UxY8MsKTISKTmtX9GX4KNZFQg+PjqvhBTAxQAeAzADYEXGcecDeBLAdgDX6Z6/biEVLGLDotNxPLsqrT6aVYHgozGvEtIB1MOjAP4zgI2qA4ioA+DzAC4AcAqAPyaiU6pJnuANY2PAhg3A6ChAFP3dsCHar0unY3ZNImD9erPfqBgZMdsvHMbGq68KikS2posTfQ/Af2XmqZTvzgLwUWb+j73P1wMAM38877wrVqzgqak5pxTaCpH5b2yVi8lJYO1aYP/+I/uGh/1VBCETItrEzCuS++uySHVYDOCZ2OfdvX2CYMboqJvjJyeBJUuAgYHo7+Tk3GNCMquEwjgTUiK6j4geTdlWO7reWiKaIqKpPXv2uLiENZLl7+qr88ujkEBHxPqsXx9ZgXGGh4Fzz51rrQ4P6zXr+5bm9HRkvU5PR59VYrprFzAzE/0VEc3E5NV6Q5rjtKoNwPegCDYBOAvAvbHP1wO4Xue8PgebdDre1+1Q954iUYisfqRFIvI+hpQbgI8BpjjwKWp/+OLZQjoPwE4AJwEYArAFwDKd8/ospLpDQaU8ZuCDiEk03gjd+sqHV5uFSkhr8ZES0YVEtBuR1fmPRHRvb/9riOhuAGDmgwCuAXAvgCcA/G9mfqyO9Nrk6aftHtdKVA+nyocm0fjD5DXFTbwgPrzaQqSpa+ibWKQNxwezxfc2aEXoPAaT1+XDq80CPlmkbSYt7pFEN94BBOqYL4sqeGSr76cOEo3H5CSwZs3snl1A9HnduiOfTaxMH15tIdLUNfTNZ4uUOX2CdJuz4xQ9X1C0fuxsveQFTeOuYp05SW2UhyqAj8EmV5vvQhrHxTBumYfYMrbmTvUQ250W0pripstv+ZxfRUg9pGwmKruqsKCByUsKTBXKJDcr76Wdoy/YwJEJt0KcKlKE1EPKOtZNZtWXXjkFaVKkJEGZ5Kp+2+mohbgJk5erhFSCTTVStqtHmmNeNaw8q1dOKwNWupi8pMD67pRJrioodPvt6njbunVzA1MqQutFJkJaI2W7IqYFjq+6yizqadLHr5WYvKTA+paWSW6RTgu69UkQUfokaWZq6FsoTXtXLjWTAEJgrdHqER+pNVR5LaQlxyE+Uj+pO8grIx01KBi1f6E7yh/sTngtEFXmP9vCXUfZESEVUsmySOsWee8weCCBGaeVMDExO0rf7ZYT0TqerwipkEpWp34RghiGJbdNLhOd+sW28NX1fEVIBSVpBcF0NErjBdaw5Np2mfj6vHUF0rbw1eWSEiEVjMjKqK1sthqWXJvC4fPz1q1w044pI3xikYqQBkFWRm1Ts/UwhjdtU/x8ft4qgQT0OuAXvQfxkYqQBkFWRm1lpL9AybXVHPf5efeHeya3Tid/5F1Z4ZOovQhpEKgyqs8WklNqclRW+bxNbzFLKLPG4/vk5zVBhLSFuCr3NptVvgZRfKKqZmyR67TNBSRC2jJcFz4bAuhzEMU3ijxv098UEb4mTZGngwhpy7BhDbi2FptosfiCqYhNTKS/Cx1fbFY+aVqLQ4S0ZZQNUFRhTRRNYxWFM3QBMKmk8qLrUrEdQYS0Zbia69RmobLdlLRFE5qkJpVUVnQ9tPt2jQhpg0mznsqKgapgAXbTbTO4YYsmuBxM7iErui4iOhsR0oaS5+wv2jzN6h9oO/0maayiT6XP/TZ1ScsX/ftKPucmVBxV4ZWQArgYwGMAZgCsyDhuF4CtADarbiBta4qQ6oiMi0KQFXiwaZEWQSxSfeLDM7MWRGyCK6MqfBPSNwJ4PYDvaQjpQtPzN0FIdTO3i8kxfAs8xCuUbpd5cNBtoW+asOhUDKEH16rCKyE9fHERUiW6VpFt68m3wEOaqA0NRYJatg9rlnA0RVjKdGsS5hKqkD4F4GEAmwCszTnXWgBTAKZGRkasP8Cq0bU0bY8yymrS1yEmrlwXTbI4VeS1LrrdulMYHpULKYD7ADyasq2OHZMnpIt7f38HwBYAb9e5dpssUmZ3o4zqbtIzuwn8hOYDLfp+VWvGxy37plUerlEJ6Tzj1fI0YeZ3WjjHs72/PyeibwBYCWBj2fOGwPr10Wqe8eVrVasrjo1lr96oQ9ZSuXWu6jgyEq1smra/KCGtmtxf5bX/bvqrvALZ73xyEti7N/vcCxYcwP79u/HEEy/bSWyDmD9/Pk444QQMDg7q/SBNXavakGGRAlgA4OjY/98HcL7OeZtgkTJX66fztS+hi2Z4SBZp0bTmTWEHMN94407+wQ/28MzMTAV3Eg4zMzO8Z88e3rlz55zvoLBIa1nXnoguJKLdAM4C8I9EdG9v/2uI6O7eYccD+Bci2gLgQQD/yMz31JHeuhgbA3btAmZmor9lrc4sVBbe6Kjb68aZnASWLAEGBqK/k5Oz108HgE4nss7WrYu+L8L69ZGVHcfXtdSLWs861vVrX/syXvnKLojIPGENhojQ7Xbx8ssGlnqauoa+NcUirRJdy6+uqflsW6Y+ROVd9hPWsUjvuedxfv5567fVGB5//PE5++Bj1N7V1hYhtSkGExP5S+W6jHbnCUZIzXEdTCquIs887XeDg7O7jT300FyhqJrnnnuO/+iP/oiXLl3Kp59+Ol9wwQX85JNP8lNPPcXLli1zcs2XX36ZL7nkEj755JN55cqV/NRTT6UeJ0LaAiG13e3JxUqQJkKf5aPN+842VVirVfTKyPtdmlCUOZ8pMzMzfOaZZ/LNN998eN/mzZt548aNToX085//PH/gAx9gZuY77riDL7nkktTjREhbIKQ2LTTdc5l0RTIVep2maBUWaVV9TH0Yz28ipC6ey/33389ve9vbUr+LC+lTTz3FZ599Np922ml82mmn8b/+678yM/NPfvITftvb3sbLly/nZcuW8caNG/ngwYO8Zs0aXrZsGZ966qn8mc98Zs65zzvvPP7+97/PzMwHDhzgbrebGnATIW2BkNosiLrnMhHvItZr3oqTyc2FwBWd2i8+hFVn1JUPrgoTIXWR3htvvJGvvfba1O/iQvriiy/ySy+9xMzM27Zt4375/vSnP8033HADMzMfPHiQf/WrX/HU1BS/853vPHyeX/7yl3POvWzZMn7mmWcOf166dCnv2bNnznEmQlpL1F4ojyrKXqR/pe65TKLdptHmeHReN4j8ylfqHWdCWp9VQJ3ufj/P6elIWvbujTbmI30+03oX6DzLtF4MdVFn39sDBw7g/e9/P970pjfh4osvxuOPPw4AOOOMM/DlL38ZH/3oR7F161YcffTRWLp0KXbu3IkPfvCDuOeee3DMMce4TyAgFmmo1OEj7R+r4ydzNbF01ixGZZmYUFvnqnTruCSK+JCr6EVRt0V63333aTXt/+qv/oo//OEP86FDh/jAgQPcic3l+Oyzz/KGDRt4+fLlfPvttzMz8wsvvMB33nknr169mt/3vvfNObc07UVIZ2E7am8zkFBW6E2a+mWbw/Hp5lTirUp3ViCsjLtFd8amMs+4bh/pzMwMr1y5kr/4xS8e3rdly5Y5waZrr72WP/3pTzMz86233sqR/ce8a9cuPnjwIDMzf+5zn+MPfehDvGfPHt63bx8zM2/dupWXL18+57o33XTTrGDTxRdfnJo+EdKWCKnvlBXnZJcsm0IVv4aOYKsoY5FmoTPSrKyVWHfUnjmyKC+++GJeunQpn3LKKbxq1Sretm3bLCHdtm0bv+lNb+I3v/nN/JGPfIQXLFjAzMy33XYbL1u2jN/ylrfw2WefzTt37uTNmzfzaaedxsuXL+fly5fz3XffPeeaL730El900UV88skn8xlnnME7duxITZsIqQhpY3AlVLbOnyfERScG0ZnOsGzA0VRI24YEm4RacBEcyQtmlB3aWfb8ySGsSZiLpSstGNWnP0TWZsBRKEmauoa+iUVaPa76X2ZZZjaalzbPbzsgkzcpc5U+0jYiTXsR0spx1S8ySyxczcOaJ0aq69Yxd2pVUfs2IkIqQlo5LkfqpImF7e5fumKUdV1VYMzX2fxFSLMRIRUhrZyqR+rUNTJIdd1uNwosJfcPDtrpSuZi7L8IaTYSbBIqp+o5PusaaaM6/969wG9/O3f/MceUn8+1ynlphWKIkApWSA7xHB2NPrsq9HVFrE3P/4tfuElHU/jpT3+KSy+9FCeffDLe+ta3YtWqVdi2bRt27dqFU0891ck1N27ciNNPPx3z5s3DnXfeaeWcIqSCNaq0nOqa5V513W43/fiiwu7TOPvDWE4UM+PCCy/EOeecgx07dmDTpk34+Mc/jp/97GdWkqtiZGQEt912G/7kT/7E3knT2vuhb+IjbQd1zXJfRfCriqn8jHykDhJV1zR6fdasWcNf//rXld9LsEmEtHZ8WMqjamzdc1WBNCMhdZCouqbR62NTSJ0txyy0l6JLCIeOjWWxAU+Xi64xUQcOHMA111yDzZs3o9PpYNu2bQCiafQuv/xyHDhwAO9+97vxlre8ZdY0eu9617tw3nnnOU8fID5SwQHr1h0R0T79YY1CPl4O/XSQqGXLlmHTpk25x/31X/81jj/+eGzZsgVTU1P4ba97xNvf/nZs3LgRixcvxmWXXYavfOUrOPbYY7Flyxacc845uOWWW3DllVcWTp8JIqSCdby0qALCy+WiHSTqHe94B37zm99gw4YNh/c98sgj+Od//udZx+3btw+LFi3CwMAAvvrVr+LQoUMAgOnpaRx//PF4//vfjyuvvBIPP/wwnn/+eczMzOA973kPbrjhBjz88MOF02dEWnvf9QbgUwB+BOARAN8A8CrFcecDeBLAdgDX6Z5ffKT14sMyGqFThY/ZuEO+g0TVMY3egw8+yIsXL+bh4WE+7rjj+JRTTklNm4mPlKLvqoWIzgPwHWY+SESf6An6XySO6QDYBuA/ANgN4CEAf8zMj+edf8WKFTw1NWU/4YIWSR8pEBkvLvuVCuY88cQTeOMb31h3Mrwl7fkQ0SZmXpE8tpamPTP/EzMf7H18AMAJKYetBLCdmXcy828B/C2A1VWlUShO1Z3zBaFufIjaXw7gayn7FwN4JvZ5N4DfqyRFQmlsRbAFIQScCSkR3Qfgd1O+WsfM/9A7Zh2AgwBKj9sgorUA1gLRyAVBEISqcCakzPzOrO+J6DIA/wnAuZzuqH0WwImxzyf09qmutwHABiDykZqmVxDaCDODdNe/bhGmsaNafKREdD6AjwD4Q2berzjsIQCvI6KTiGgIwKUA7qoqjYLQdObPn4+9e/cai0bTYWbs3bsX8+fP1/5NXT7SmwC8AsC3e7XhA8x8FRG9BsCXmHlVL6J/DYB7AXQA3MrMj9WUXkFoHCeccAJ2796NPXv21J0U75g/fz5OOCEtBp5OLULKzK9V7P8JgFWxz3cDuLuqdAlCmxgcHMRJJ51UdzIagYxsEgRBKIkIqSAIQklESAVBEEpSyxBR1xDRHgDTBj9ZCOB5R8mR6/t9/Tbfe9uvX+Tao8z86uTORgqpKUQ0lTZ+Vq7f/Ou3+d7bfn2b15amvSAIQklESAVBEEoiQhqxIf8QuX5Dr9/me2/79a1dW3ykgiAIJRGLVBAEoSStFFIi+hQR/YiIHiGibxDRqxTHnU9ETxLRdiK6zuL1Lyaix4hohoiUUUMi2kVEW4loMxFZm/Lf4Pqu7v84Ivo2Ef249/dYxXGHeve+mYhKTViTdy9E9Aoi+lrv+x8S0ZIy1ytw/cuIaE/sfq2t2kZEtxLRz4noUcX3RESf7aXtESI63da1Na9/DhHti937X1q89olE9F0ieryX5z+Uckz5+09bf6TpG4DzAMzr/f8JAJ9IOaYDYAeApQCGAGwBcIql678RwOsBfA/AiozjdgFY6OD+c6/v+P4/id4aXACuS3v+ve9+bel6ufcC4GoAt/T+vxTA1yw+b53rXwbgJtvvunfutwM4HcCjiu9XAfgWAAJwJoAfVnz9cwB809G9LwJweu//oxEtX5R89qXvv5UWKde81AkzP8HMT9o4l8Pru1zqZTWA23v/3w7g3ZbOq0LnXuJpuhPAuWRvos5al81h5o0AfpFxyGoAX+GIBwC8iogWVXh9ZzDzc8z8cO//FwA8gWj1jTil77+VQprgckS1UZK0pU6SL8A1DOCfiGhTbwWAKnF5/8cz83O9/38K4HjFcfOJaIqIHiCiMmKrcy+Hj+lVsvsAdEtc0/T6APCeXtPyTiI6MeV7V/iQ188ioi1E9C0iWubiAj13zWkAfpj4qvT9+7BmkxOqXuqkyPU1OJuZnyWi30E0d+uPerV7VdcvTNb14x+YmYlI1XVktHf/SwF8h4i2MvMO22n1hP8L4A5m/g0RfQCRdfyOmtNUFQ8jete/JqJVAP4PgNfZvAARHQXg7wBcy8y/snluoMFCyhUvdWJ6fc1zPNv7+3Mi+gaiJqKWkFq4vrP7J6KfEdEiZn6u14T6ueIc/fvfSUTfQ2RNFBFSnXvpH7ObiOYB+HcA9ha4VqHrM3P8Wl9C5EeuilLvuixxYWPmu4noC0S0kJmtjMEnokFEIjrJzH+fckjp+29l054CWOqEiBYQ0dH9/xEFyFKjno5wef93AVjT+38NgDkWMhEdS0Sv6P2/EMAfAHi84PV07iWeposAfEdRwTq5fsIn94eIfHlVcReAP+tFr88EsC/menEOEf1u3x9NRCsR6ZKVSqx33r8B8AQzf0ZxWPn7dxEp830DsB2RT2Rzb+tHa18D4O7YcasQRfl2IGoS27r+hYj8ML8B8DMA9yavjyjCu6W3PVb19R3ffxfA/QB+DOA+AMf19q9AtNQMAPw+gK29+98K4IqS15xzLwA+hqgyBYD5AL7eyxsPAlhqOc/lXf/jvfe8BcB3AbzB4rXvAPAcgAO9934FgKsAXNX7ngB8vpe2rcjoSeLo+tfE7v0BAL9v8dpnI4o1PBIr76ts37+MbBIEQShJK5v2giAINhEhFQRBKIkIqSAIQklESAVBEEoiQioIglASEVKh1RDRPUT0b0T0zbrTIoSLCKnQdj4F4L11J0IIGxFSoRUQ0Rm9CUHm90aNPUZEpzLz/QBeqDt9Qtg0dqy9IMRh5ocomhz6BgCvBDDBzFUOuRUajAip0CY+hmjc+8sA/rzmtAgNQpr2QpvoAjgK0Uzp82tOi9AgREiFNvFFAP8D0fyzn6g5LUKDkKa90AqI6M8AHGDm/0VEHQDfJ6J3APifAN4A4Cgi2o1olql760yrEB4y+5MgCEJJpGkvCIJQEhFSQRCEkoiQCoIglESEVBAEoSQipIIgCCURIRUEQSiJCKkgCEJJREgFQRBK8v8BLFCoTjG3IfcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Import Data and train/test split; plot the data\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "data_lin_sep_svm = pd.read_csv(\"./data/kernelized_svm/circles.csv\")\n",
    "X = data_lin_sep_svm.iloc[:,:2]\n",
    "y = data_lin_sep_svm[\"y\"]\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, stratify=y, test_size=0.2, random_state=1)\n",
    "sc = StandardScaler()\n",
    "X_train_sc = sc.fit_transform(X_train)\n",
    "X_test_sc = sc.transform(X_test)\n",
    "\n",
    "plt.figure(figsize=(5,5))\n",
    "plt.plot(X_train_sc[y_train==0,0], X_train_sc[y_train==0,1], \"bo\", label=\"Class 0\")\n",
    "plt.plot(X_train_sc[y_train==1,0], X_train_sc[y_train==1,1], \"ro\", label=\"Class 1\")\n",
    "plt.xlabel(\"x1\")\n",
    "plt.ylabel(\"x2\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVC(C=0.5, break_ties=False, cache_size=200, class_weight=None, coef0=0.0,\n",
       "    decision_function_shape='ovr', degree=3, gamma=0.5, kernel='rbf',\n",
       "    max_iter=-1, probability=False, random_state=None, shrinking=True,\n",
       "    tol=0.001, verbose=False)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Call and train SVM with rbf kernel\n",
    "from sklearn.svm import SVC \n",
    "rbf_svm = SVC(kernel='rbf', gamma=.5, C=.5)\n",
    "rbf_svm.fit(X_train_sc, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's visualize the estimated decision functions $f(\\mathbf{x})$ for the first five test units: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.47902247,  0.9940158 , -1.2705425 ,  0.89898439,  1.47600071])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rbf_svm.decision_function(X_test_sc[:5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "...and the corresponding predictions: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 0, 1, 1])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rbf_svm.predict(X_test_sc[:5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unfortunately, when the `kernel` used is not `linear`, we can't retrieve the model coefficients (as explained also in the function documentation)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# This will give an error: \n",
    "# rbf_svm.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, we can retrieve the support vectors (here we only see the first 5): "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.47574798, -0.2118328 ],\n",
       "       [ 1.71357044,  0.23386059],\n",
       "       [ 0.89408964, -1.40208169],\n",
       "       [-0.47869547, -1.38586499],\n",
       "       [ 0.20742308,  1.55501125]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rbf_svm.support_vectors_[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's plot the model's decision boundaries and the margins, highlighting the support vectors. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xx, yy = np.meshgrid(np.arange(X_train_sc[:,0].min(), X_train_sc[:,0].max(), 0.1),\n",
    "                     np.arange(X_train_sc[:,1].min(), X_train_sc[:,1].max(), 0.1))\n",
    "zz = rbf_svm.decision_function(np.c_[xx.ravel(),yy.ravel()]).reshape(xx.shape)\n",
    "\n",
    "plt.figure(figsize=(6,6))\n",
    "contour = plt.contour(xx, yy, zz, levels=[-1,0,1], alpha=1., vmin=0, vmax=1, linewidths=2, colors='k', linestyles='-')\n",
    "plt.clabel(contour, inline=1, fontsize=15, colors='k')\n",
    "plt.plot(X_train_sc[y_train==0,0], X_train_sc[y_train==0,1], \"bo\", label=\"Class 0\")\n",
    "plt.plot(X_train_sc[y_train==1,0], X_train_sc[y_train==1,1], \"ro\", label=\"Class 1\")\n",
    "plt.plot(rbf_svm.support_vectors_[:,0], rbf_svm.support_vectors_[:,1], \"yo\", markerfacecolor='none', markersize=13, \n",
    "        label=\"Support Vectors\")\n",
    "plt.xlabel(\"x1\")\n",
    "plt.ylabel(\"x2\")\n",
    "plt.ylim(-2.7,2.5)\n",
    "plt.xlim(-2.7,2.5)\n",
    "plt.legend(loc=3,  frameon=False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Last, let's assess the accuracy of the model on the test set: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rbf_svm.score(X_test_sc,y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercises**. Try out different values of the `gamma` hyperparameter, and see how the perofrmance and decision boundaries change. Next, try with `kernel=poly` and different levels of `degree`. Last, try also with `kernel=linear`. In all these cases, manipulate also the regulazitation parameter `C`, and compare results. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.2 Multiclass case \n",
    "We are now just going to have a quick view of the model output in the multiclass case. We will use the `make_blob` function from scikit-learn in order to generate a synthetic dataset. This time we will try SVM with a polynomial kernel of degree 2, and C=1. As you can read from the documentation, multiclass SVC is always estimated with a 'ovo' (one-versus-one) approach (due to computational reasons). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import make_blobs\n",
    "X, y = make_blobs(n_samples=200, centers=4, cluster_std=1, random_state=2)\n",
    "y = y % 3\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, stratify=y, test_size=0.2, random_state=1)\n",
    "sc = StandardScaler()\n",
    "X_train_sc = sc.fit_transform(X_train)\n",
    "X_test_sc = sc.transform(X_test)\n",
    "\n",
    "# Draw Data\n",
    "plt.figure(figsize=(5,5))\n",
    "plt.plot(X_train_sc[y_train==0,0], X_train_sc[y_train==0,1], \"bo\", label=\"Class 0\")\n",
    "plt.plot(X_train_sc[y_train==1,0], X_train_sc[y_train==1,1], \"ro\", label=\"Class 1\")\n",
    "plt.plot(X_train_sc[y_train==2,0], X_train_sc[y_train==2,1], \"go\", label=\"Class 2\")\n",
    "plt.xlabel(\"x1\")\n",
    "plt.ylabel(\"x2\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVC(C=1, break_ties=False, cache_size=200, class_weight=None, coef0=0.0,\n",
       "    decision_function_shape='ovr', degree=2, gamma='scale', kernel='poly',\n",
       "    max_iter=-1, probability=False, random_state=None, shrinking=True,\n",
       "    tol=0.001, verbose=False)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Train SVC with polynomial kernel ('ovo' estimation)\n",
    "poly_svm = SVC(kernel=\"poly\", degree=2, C=1)\n",
    "poly_svm.fit(X_train_sc, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the decision function for the first five test units:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.22011423,  2.2493756 ,  0.8311857 ],\n",
       "       [ 2.26736387, -0.26452675,  0.94252605],\n",
       "       [-0.18863002,  0.85422611,  2.22513557],\n",
       "       [ 2.30595862, -0.28781329,  0.72360872],\n",
       "       [-0.22491713,  0.92312336,  2.23454846]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly_svm.decision_function(X_test_sc[:5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, decision functions are class-specific. The predictions, as always, can be inspected with the `predict` method: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 2, 0, 2])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly_svm.predict(X_test_sc[:5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And the test set accuracy: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly_svm.score(X_test_sc, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xx, yy = np.meshgrid(\n",
    "        np.linspace(X_train_sc[:,0].min()-0.1, X_train_sc[:,0].max()+0.1, 500).reshape(-1, 1),\n",
    "        np.linspace(X_train_sc[:,1].min()-0.1, X_train_sc[:,1].max()+0.1, 500).reshape(-1, 1),\n",
    ")\n",
    "zz = poly_svm.predict(np.c_[xx.ravel(), yy.ravel()]).reshape(xx.shape)\n",
    "\n",
    "plt.figure(figsize=(5, 5))\n",
    "plt.contour(xx, yy, zz, alpha=0.25, colors='k')\n",
    "plt.plot(X_train_sc[y_train==0,0], X_train_sc[y_train==0,1], \"bo\", label=\"Class 0\")\n",
    "plt.plot(X_train_sc[y_train==1,0], X_train_sc[y_train==1,1], \"ro\", label=\"Class 1\")\n",
    "plt.plot(X_train_sc[y_train==2,0], X_train_sc[y_train==2,1], \"go\", label=\"Class 2\")\n",
    "\n",
    "plt.xlabel(\"x1\")\n",
    "plt.ylabel(\"x2\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**. Try out different values for the polynomial kernel, different values of C, and different kernels. Compare the results. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7. Application to the Heart Dataset \n",
    "We are now going to cross-validate several SVM models, with varying kernels, on the Heart data. The goal is to find which is the best combination of kernel+hyperparameter values, in order to discover what type of relationships might be present between the features and the presence/absence of heart disease. \n",
    "\n",
    "We will make use of the following grid: \n",
    "* RBF kernel, with gamma= 0.01, 0.1, 0.5, 1., 5.\n",
    "* polynomial kernel, with degree=1, 2, 3, and 10 \n",
    "* linear kernel\n",
    "* for all kernels above, C will be set equal to 0.001, 0.01, 0.1, 0.5, 2, and 10.\n",
    "\n",
    "Validation will be performed with 10-fold-CV. In order to keep track of what GridSearchCV is doing, we will also set the `verbose` parameter. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load datasets\n",
    "data_train = pd.read_csv(\"./data/heart_data/heart_train_processed.csv\")\n",
    "data_test = pd.read_csv(\"./data/heart_data/heart_test_processed.csv\")\n",
    "X_train = data_train.drop(\"y\", axis=1)\n",
    "X_test = data_test.drop(\"y\", axis=1)\n",
    "y_train = data_train[\"y\"]\n",
    "y_test = data_test[\"y\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting 10 folds for each of 66 candidates, totalling 660 fits\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=-1)]: Using backend LokyBackend with 4 concurrent workers.\n",
      "[Parallel(n_jobs=-1)]: Done  38 tasks      | elapsed:    1.0s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CV Grid Search: Done\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=-1)]: Done 660 out of 660 | elapsed:    2.0s finished\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import GridSearchCV\n",
    "# Set parameter grid \n",
    "C_grid = [1e-3, 1e-2, 1e-1, 5e-1, 2, 10]\n",
    "tuning_parameters = [{'kernel': ['rbf'], 'gamma': [1e-3, 1e-2, 1e-1, 5e-1, 1., 5.], 'C': C_grid},\n",
    "                    {'kernel': ['poly'], 'degree': [1, 2, 3, 10], 'C':C_grid}, \n",
    "                    {'kernel': ['linear'], 'C': C_grid}]\n",
    "\n",
    "# Launch GridSearchCV\n",
    "clf = GridSearchCV(SVC(), tuning_parameters, cv=10, n_jobs=-1, verbose=2 )\n",
    "clf.fit(X_train, y_train)\n",
    "print(\"CV Grid Search: Done\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The best estimator found with grid search is: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVC(C=0.5, break_ties=False, cache_size=200, class_weight=None, coef0=0.0,\n",
       "    decision_function_shape='ovr', degree=1, gamma='scale', kernel='poly',\n",
       "    max_iter=-1, probability=False, random_state=None, shrinking=True,\n",
       "    tol=0.001, verbose=False)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clf.best_estimator_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Which is a polynomial kernel of degree 1: this corresponds to a SVM algorithm with linear kernel (or, equivalently, to a linear SVM algorithm). The best performing model leads to the CV accuracy: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8478333333333333"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clf.best_score_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Which is in line, indeed, with what we have observed with the linear models. This can suggest that linear relationships are actually the best suited one to describe the relationships between the predictors in the dataset and the presence/absence of heart disease. Let's compare the performance of the estimated models:  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cv_res = pd.DataFrame(clf.cv_results_).sort_values(by=\"mean_test_score\", ascending=False)\n",
    "plt.figure(figsize=(15,5))\n",
    "x_ax = np.linspace(0, cv_res.shape[0], cv_res.shape[0])\n",
    "plt.errorbar(x_ax, cv_res[\"mean_test_score\"], yerr=cv_res[\"std_test_score\"], ecolor='g')\n",
    "plt.plot(x_ax, cv_res[\"mean_test_score\"], \"b-\")\n",
    "plt.plot(np.argmax(cv_res[\"mean_test_score\"].to_numpy()), clf.best_score_, \"ro\", label=\"Best CV Estimator\")\n",
    "plt.xticks(x_ax, (cv_res[\"params\"]), rotation=90, fontsize=9)\n",
    "plt.xlabel(\"Hyperparameter Set\")\n",
    "plt.ylabel(\"CV Accuracy\")\n",
    "plt.title(\"SVM: CV Accuracy -/+ 1.STD (sorted by score)\")\n",
    "plt.legend(loc=3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the two best performing models are indeed linear models. However, they also have large standard errors in their CV accuracies, which potentially makes SVM algorithms with RBF kernels also good candidates to describe the mechanism that govern the presence/absence of heart disease in the patients of this dataset.\n",
    "\n",
    "Last, let's check the accuracy of the best performing model on the test set: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8524590163934426"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clf.best_estimator_.score(X_test, y_test)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}