{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Logistic Classification\n", "=======================\n", "\n", "*Important:* Please read the [installation page](http://gpeyre.github.io/numerical-tours/installation_python/) for details about how to install the toolboxes.\n", "$\\newcommand{\\dotp}[2]{\\langle #1, #2 \\rangle}$\n", "$\\newcommand{\\enscond}[2]{\\lbrace #1, #2 \\rbrace}$\n", "$\\newcommand{\\pd}[2]{ \\frac{ \\partial #1}{\\partial #2} }$\n", "$\\newcommand{\\umin}[1]{\\underset{#1}{\\min}\\;}$\n", "$\\newcommand{\\umax}[1]{\\underset{#1}{\\max}\\;}$\n", "$\\newcommand{\\umin}[1]{\\underset{#1}{\\min}\\;}$\n", "$\\newcommand{\\uargmin}[1]{\\underset{#1}{argmin}\\;}$\n", "$\\newcommand{\\norm}[1]{\\|#1\\|}$\n", "$\\newcommand{\\abs}[1]{\\left|#1\\right|}$\n", "$\\newcommand{\\choice}[1]{ \\left\\{ \\begin{array}{l} #1 \\end{array} \\right. }$\n", "$\\newcommand{\\pa}[1]{\\left(#1\\right)}$\n", "$\\newcommand{\\diag}[1]{{diag}\\left( #1 \\right)}$\n", "$\\newcommand{\\qandq}{\\quad\\text{and}\\quad}$\n", "$\\newcommand{\\qwhereq}{\\quad\\text{where}\\quad}$\n", "$\\newcommand{\\qifq}{ \\quad \\text{if} \\quad }$\n", "$\\newcommand{\\qarrq}{ \\quad \\Longrightarrow \\quad }$\n", "$\\newcommand{\\ZZ}{\\mathbb{Z}}$\n", "$\\newcommand{\\CC}{\\mathbb{C}}$\n", "$\\newcommand{\\RR}{\\mathbb{R}}$\n", "$\\newcommand{\\EE}{\\mathbb{E}}$\n", "$\\newcommand{\\Zz}{\\mathcal{Z}}$\n", "$\\newcommand{\\Ww}{\\mathcal{W}}$\n", "$\\newcommand{\\Vv}{\\mathcal{V}}$\n", "$\\newcommand{\\Nn}{\\mathcal{N}}$\n", "$\\newcommand{\\NN}{\\mathcal{N}}$\n", "$\\newcommand{\\Hh}{\\mathcal{H}}$\n", "$\\newcommand{\\Bb}{\\mathcal{B}}$\n", "$\\newcommand{\\Ee}{\\mathcal{E}}$\n", "$\\newcommand{\\Cc}{\\mathcal{C}}$\n", "$\\newcommand{\\Gg}{\\mathcal{G}}$\n", "$\\newcommand{\\Ss}{\\mathcal{S}}$\n", "$\\newcommand{\\Pp}{\\mathcal{P}}$\n", "$\\newcommand{\\Ff}{\\mathcal{F}}$\n", "$\\newcommand{\\Xx}{\\mathcal{X}}$\n", "$\\newcommand{\\Mm}{\\mathcal{M}}$\n", "$\\newcommand{\\Ii}{\\mathcal{I}}$\n", "$\\newcommand{\\Dd}{\\mathcal{D}}$\n", "$\\newcommand{\\Ll}{\\mathcal{L}}$\n", "$\\newcommand{\\Tt}{\\mathcal{T}}$\n", "$\\newcommand{\\si}{\\sigma}$\n", "$\\newcommand{\\al}{\\alpha}$\n", "$\\newcommand{\\la}{\\lambda}$\n", "$\\newcommand{\\ga}{\\gamma}$\n", "$\\newcommand{\\Ga}{\\Gamma}$\n", "$\\newcommand{\\La}{\\Lambda}$\n", "$\\newcommand{\\si}{\\sigma}$\n", "$\\newcommand{\\Si}{\\Sigma}$\n", "$\\newcommand{\\be}{\\beta}$\n", "$\\newcommand{\\de}{\\delta}$\n", "$\\newcommand{\\De}{\\Delta}$\n", "$\\newcommand{\\phi}{\\varphi}$\n", "$\\newcommand{\\th}{\\theta}$\n", "$\\newcommand{\\om}{\\omega}$\n", "$\\newcommand{\\Om}{\\Omega}$\n", "$\\newcommand{\\eqdef}{\\equiv}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This tour details the logistic classification method (for 2 classes and\n", "multi-classes).\n", "\n", "\n", "_Warning:_ Logisitic classification is actually called [\"logistic\n", "regression\"](https://en.wikipedia.org/wiki/Logistic_regression) in the literature, but it is in fact a classification method.\n", "\n", "\n", "We recommend that after doing this Numerical Tours, you apply it to your\n", "own data, for instance using a dataset from [LibSVM](https://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/).\n", "\n", "_Disclaimer:_ these machine learning tours are intended to be\n", "overly-simplistic implementations and applications of baseline machine learning methods.\n", "For more advanced uses and implementations, we recommend\n", "to use a state-of-the-art library, the most well known being\n", "[Scikit-Learn](http://scikit-learn.org/)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%load_ext autoreload\n", "%autoreload 2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We define a few helpers." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def find(x): return np.nonzero(x)[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Two Classes Logistic Classification\n", "-----------------------------------\n", "Logistic classification is, with [support vector machine (SVM)](https://en.wikipedia.org/wiki/Support_vector_machine), the baseline\n", "method to perform classification. Its main advantage over SVM is that is\n", "is a smooth minimization problem, and that it also output class\n", "probabity, offering a probabilistic interpretation of the classification.\n", "\n", "\n", "To understand the behavior of the method, we generate synthetic data\n", "distributed according to a mixture of Gaussian with an overlap governed by an offset $\\omega$.\n", " Here classes indexes are set to $y_i \\in\n", "\\{-1,1\\}$ to simplify the equations." ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "n = 1000 # number of sample\n", "p = 2 # dimensionality\n", "omega = np.array([1,.5])*2.5 # offset \n", "n1 = int(n/2)\n", "X = np.vstack(( np.random.randn(n1,2), np.random.randn(n1,2)+np.ones([n1,1])*omega ))\n", "y = np.vstack(( np.ones([n1,1]), -np.ones([n1,1]) ))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the classes." ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": 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C56O41+dUUIYxBWVxwy4A1nx0yfrFCNEoiJqL3V97AXeujcYNwPDb6egcJvHo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\n5IxEh0e6BC3tBiQkMkamGvtvAeQCeJsQAgBVlNLvZbwricw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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "I = find(y==-1)\n", "J = find(y==1)\n", "plt.clf\n", "plt.plot(X[I,0], X[I,1], '.')\n", "plt.plot(X[J,0], X[J,1], '.')\n", "plt.axis('equal');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Logistic classification minimize a logistic loss in place of the usual\n", "$\\ell^2$ loss for regression\n", " $$ \\umin{w} E(w) \\eqdef \\frac{1}{n} \\sum_{i=1}^n L(\\dotp{x_i}{w},y_i) $$\n", "where the logistic loss reads\n", " $$ L( s,y ) \\eqdef \\log( 1+\\exp(-sy) ) $$\n", "This corresponds to a smooth convex minimization. If $X$ is injective,\n", "this is also strictly convex, hence it has a single global minimum.\n", "\n", "\n", "Compare the binary (ideal) 0-1 loss, the logistic loss and the\n", "\n", "(the one used for SVM)." ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "image/png": 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bxtCgdANGNRvloEKFo0m4C+EpUq7Bsn4Q8zO0ewPuG5brQySlJjF4/WAKeRVi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\nzQj0snXMrdHO0qw613eoXrl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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = np.linspace(-3,3,255).transpose()\n", "plt.clf\n", "plt.plot(t, t>0)\n", "plt.plot(t, np.log(1+np.exp(t)))\n", "plt.plot(t, np.maximum(t,0) )\n", "plt.axis('tight');\n", "plt.legend(['Binary', 'Logistic', 'Hinge']);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This can be interpreted as a when one\n", "models the probability of belonging to the two classes for sample $x_i$ as\n", " $$ h(x_i) \\eqdef (\\th(x_i),1-\\th(x_i)) \\qwhereq\n", " \\th(s) \\eqdef \\frac{e^{s}}{1+e^s} = (1+e^{-s})^{-1} $$\n", "\n", "\n", "Re-writting the energy to minimize\n", " $$ E(w) = \\Ll(X w,y) \\qwhereq \\Ll(s,y)= \\frac{1}{n} \\sum_i L(s_i,y_i), $$\n", "its gradient reads\n", " $$ \\nabla E(w) = X^\\top \\nabla \\Ll(X w,y)\n", " \\qwhereq\n", " \\nabla \\Ll(s,y) = \\frac{y}{n} \\odot \\th(-y \\odot s), $$\n", "where $\\odot$ is the pointwise multiplication operator, i.e. * in\n", "Python.\n", "\n", "\n", "Define the energies." ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [], "source": [ "def L(s,y): return 1/n * sum( np.log( 1 + np.exp(-s*y) ) )\n", "def E(w,X,y): return L(X.dot(w),y);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define their gradients." ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [], "source": [ "def theta(v): return 1 / (1+np.exp(-v))\n", "def nablaL(s,r): return - 1/n * y * theta(-s * y)\n", "def nablaE(w,X,y): return X.transpose().dot( nablaL(X.dot(w),y) )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "_Important:_ in order to improve performance, it is important (especially\n", "in low dimension $p$) to add a constant bias term $w_{p+1} \\in \\RR$, and replace $\\dotp{x_i}{w}$\n", "by $ \\dotp{x_i}{w} + w_{p+1} $. This is equivalently achieved by\n", "adding an extra $(p+1)^{\\text{th}}$ dimension equal to 1 to each\n", "$x_i$, which we do using a convenient macro." ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [], "source": [ "def AddBias(X): return np.hstack(( X, np.ones((np.size(X,0),1)) ))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With this added bias term, once $w_{\\ell=0} \\in \\RR^{p+1}$ initialized\n", "(for instance at $0_{p+1}$)," ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [], "source": [ "w = np.zeros((p+1,1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Perform one step of gradient descent reads\n", "$$ w_{\\ell+1} = w_\\ell - \\tau_\\ell \\nabla E(w_\\ell). $$" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [], "source": [ "tau = 1; # here we are using a fixed tau\n", "w = w - tau * nablaE(w,AddBias(X),y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\\tau < \\frac{2}{L}$$\n", "$$ L \\leq \\frac{1}{4}\\norm{X}^2 $$\n", "If one chooses \n", "$$\\tau < \\tau_{\\max} \\eqdef \\frac{2}{\\frac{1}{4}\\norm{X}^2},$$\n", "then one is sure that the gradient descent converges." ] }, { "cell_type": "code", "execution_count": 82, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.0014965184333816531\n" ] } ], "source": [ "np.linalg.norm(X)\n", "tau_max = 2/(1/4 * np.linalg.norm(AddBias(X), 2)**2 )\n", "print(tau_max)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Exercise 1__\n", "\n", "Implement a gradient descent\n", "$$ w_{\\ell+1} = w_\\ell - \\tau_\\ell \\nabla E(w_\\ell). $$\n", "Monitor the energy decay.\n", "Test different step size, and compare with the theory (in particular\n", "plot in log domain to illustrate the linear rate).\n", "etAR(1);\n", "etAR(1);" ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "run -i nt_solutions/ml_3_classification/exo1" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-2.41929334]\n", " [-1.0750284 ]\n", " [ 3.65553274]]\n" ] } ], "source": [ "print(w)" ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [], "source": [ "## Insert your code here." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generate a 2D grid of points." ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [], "source": [ "q = 201\n", "tx = np.linspace( X[:,0].min(), X[:,0].max(),num=q) \n", "ty = np.linspace( X[:,1].min(), X[:,1].max(),num=q) \n", "[B,A] = np.meshgrid( ty,tx )\n", "G = np.vstack([A.flatten(), B.flatten()]).transpose()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Evaluate class probability associated to weight vectors on this grid." ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [], "source": [ "Theta = theta(AddBias(G).dot(w))\n", "Theta = Theta.reshape((q,q))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Display the data overlaid on top of the\n", "classification probability, this highlight the\n", "separating hyperplane $ \\enscond{x}{\\dotp{w}{x}=0} $." ] }, { "cell_type": "code", "execution_count": 80, "metadata": {}, "outputs": [ { "data": { "image/png": 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Nlu+XdZ/eXsiI/RagVTiYHssTPNdnOlTH8+ix9l+NGs+DrMVyY9pv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\nHyodAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.clf\n", "plt.imshow(Theta.transpose(), origin=\"lower\", extent=[tx.min(),tx.max(),ty.min(),ty.max()])\n", "plt.axis('equal')\n", "plt.plot(X[I,0], X[I,1], '.')\n", "plt.plot(X[J,0], X[J,1], '.')\n", "plt.axis('off');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Exercise 2__\n", "\n", "Test the influence of the separation offset $\\omega$ on the result." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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7NkbLsV4KmTT965fHvohSYBItWh2RtMAg6LvzJifPrGHZD54n3T/sNjv3SkrR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\n0YSlbKLRzXeTz5ProOvu86qfPiawjX/B2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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "run -i nt_solutions/ml_3_classification/exo2" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "## Insert your code here." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Exercise 3__\n", "\n", "Test logistic classification on a real life dataset. You can look at the Numerical Tour on stochastic gradient descent\n", "for an example. Split the data in training and testing to evaluate the\n", "classification performance, and check the impact of regularization." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "run -i nt_solutions/ml_3_classification/exo3" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "## Insert your code here." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Kernelized Logistic Classification\n", "----------------------------------\n", "Logistic classification tries to separate the classes using\n", "a linear separating hyperplane $ \\enscond{x}{\\dotp{w}{x}=0}. $\n", "\n", "\n", "In order to generate a non-linear descision boundary, one can replace the\n", "parametric linear model by a non-linear [non-parametric](https://en.wikipedia.org/wiki/Nonparametric_statistics) model, thanks to\n", "kernelization. It is non-parametric in the sense that the number of\n", "parameter grows with the number $n$ of sample (while for the basic\n", "method, the number of parameter is $p$. This allows in particular to\n", "generate decision boundary of arbitrary complexity.\n", "\n", "\n", "The downside is that the numerical complexity of the method grows\n", "(at least) quadratically with $n$.\n", "\n", "\n", "The good news however is that thanks to the theory of\n", " [reproducing kernel Hilbert spaces](https://en.wikipedia.org/wiki/Reproducing_kernel_Hilbert_space)\n", "(RKHS), one can still compute this non-linear decision\n", "function using (almost) the same numerical algorithm.\n", "\n", "\n", "Given a kernel $ \\kappa(x,z) \\in \\RR $ defined for $(x,z) \\in \\RR^p$,\n", "the kernelized method replace the linear decision functional $f(x) =\n", "\\dotp{x}{w}$ by a sum of kernel centered on the samples\n", "$$ f_h(x) = \\sum_{i=1}^p h_i k(x_i,x) $$\n", "where $h \\in \\RR^n$ is the unknown vector of weight to find.\n", "\n", "\n", "When using the linear kernel $\\kappa(x,y)=\\dotp{x}{y}$, one retrieves\n", "the previously studied linear method.\n", "\n", "\n", "Macro to compute pairwise squared Euclidean distance matrix." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "# slow\n", "def distmat1(X,Z):\n", " D = np.zeros((X.shape[0],Z.shape[0]))\n", " for i in np.arange(0,X.shape[0]):\n", " for j in np.arange(0,Z.shape[0]):\n", " D[i,j] = np.linalg.norm( X[i,:]-Z[j,:] );\n", " return D" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "# fast\n", "from scipy import spatial\n", "def distmat(X,Z): return spatial.distance.cdist(X,Z)**2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The gaussian kernel is the most well known and used kernel\n", "$$ \\kappa(x,y) \\eqdef e^{-\\frac{\\norm{x-y}^2}{2\\sigma^2}} . $$\n", "The bandwidth parameter $\\si>0$ is crucial and controls the locality of\n", "the model. It is typically tuned through cross validation." ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "def kappa(X,Z,sigma): return np.exp( -distmat(X,Z)/(2*sigma**2) )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We generate synthetic data in 2-D which are not separable by an\n", "hyperplane." ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "n = 1000\n", "p = 2;\n", "t = 2*np.pi*np.random.randn(n1,1);\n", "R = 2.5; \n", "r = R*(1.5 + .2*np.random.randn(n1,1)); # radius\n", "X1 = np.hstack((np.cos(t)*r, np.sin(t)*r));\n", "X = np.vstack((np.random.randn(n1,2), X1))\n", "y = np.vstack(( np.ones([n1,1]), -np.ones([n1,1]) ))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Display the classes." ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "image/png": 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p8U6R4U+49+jXTdx4T59/eL55yZhlxxjn55tjW+/1UO6Ww7D793gE+JT+J26Y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\nRRZPhVLKqgxGOjC9hIqgcRftKt0BBda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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "I = find(y==-1)\n", "J = find(y==1)\n", "plt.plot(X[I,0], X[I,1], '.')\n", "plt.plot(X[J,0], X[J,1], '.')\n", "plt.axis('equal')\n", "plt.axis('off');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once avaluated on grid points, the kernel define a matrix\n", "$$ K = (\\kappa(x_i,x_j))_{i,j=1}^n \\in \\RR^{n \\times n}. $$" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "image/png": 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ousOIf6HKqhdfIuqnTi55ZSVPXfoeXsmtMCoTxUtFtdlwHS4n455DeH35G09u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s/bj2PBdM56fB2TLBUsHz+btjMmYrqwgaCL+3DXN3B+Xg0r507HXV2D+8SpGDfuQ8rSGdeL/xGA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\n4/KcE0NywExZ347XZp8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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sigma = 1;\n", "K = kappa(X,X,sigma)\n", "plt.imshow(K);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Valid kernels are those that gives rise to positive symmetric matrices\n", "$K$. The linear and Gaussian kernel are valid kernel functions. Other\n", "popular kernels include the polynomial kernel $ \\dotp{x}{y}^a $ for $a\n", "\\geq 1$ and the Laplacian kernel $ \\exp( -\\norm{x-y}^2/\\si ) $.\n", "\n", "\n", "The kernelized Logistic minimization reads\n", " $$ \\umin{h} F(h) \\eqdef \\Ll(K h,y). $$" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [], "source": [ "def F(h,K,y): return L(K.dot(h),y)\n", "def nablaF(h,K,y): return K.transpose().dot( nablaL(K.dot(h),y) )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This minimization can be related to an infinite dimensional optimization\n", "problem where one minimizes directly over the function $f$. This\n", "is shown to be equivalent to the above finite-dimenisonal optimization problem\n", "thanks to the theory of RKHS." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Exercise 4__\n", "\n", "Implement a gradient descent to minimize $F(h)$.\n", "Monitor the energy decay.\n", "Test different step size, and compare with the theory." ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "run -i nt_solutions/ml_3_classification/exo4" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [], "source": [ "## Insert your code here." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once this optimal $h$ has been found, class probability at a point\n", "$x$ are obtained as\n", " $$ (\\th(f_h(x)), 1-\\th(f_h(x)) $$\n", "where $f_h$ has been defined above.\n", "\n", "\n", "We evaluate this classification probability on a grid." ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [], "source": [ "q = 201\n", "tmax = 5\n", "t = np.linspace(-tmax,tmax,num=q)\n", "[B,A] = np.meshgrid( t,t )\n", "G = np.vstack([A.flatten(), B.flatten()]).transpose()\n", "K1 = kappa(G,X,sigma)\n", "Theta = theta( K1.dot(h) )\n", "Theta = Theta.reshape((q,q))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Display the classification probability." ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "image/png": 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DCtlqpxJfwdZtTYyXF6mv7xBs39aSiiepbd1GWA90pPj00g5fmXmP1965yOs7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\nonQMdxoL5KDvg3uUc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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.clf\n", "plt.imshow(Theta.transpose(), origin=\"lower\", extent=[-tmax, tmax, -tmax, tmax])\n", "plt.plot(X[I,0], X[I,1], '.')\n", "plt.plot(X[J,0], X[J,1], '.')\n", "plt.axis('equal')\n", "plt.axis('off');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Exercise 5__\n", "\n", "Display evolution of the classification probability with $\\sigma$" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "image/png": 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po46AzdPYzTr3Hvsa416dA0Nh+7AC9w29zL+959/y1XO3IOvZs8XA8ftP8SM7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\no+4kU2oTH/ZfRhv4qfA1DCYhcejIKGlCF3oTvOn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zDuye0dGjC2BCRtsN/lf35/hK5Z08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tnTNMPW6Cz1hsQSJmKqCJOlijxzqO6pVyVtKoFfsUTNSA38Tgv1cD0M55xglSPEO69tCgPZbaGM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\naWfqExj5AoX2VqIz856kEsj6u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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "run -i nt_solutions/ml_3_classification/exo5" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [], "source": [ "## Insert your code here." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Exercise 6__\n", "\n", "Separate the dataset into a training set and a testing set. Evaluate the classification performance\n", "for varying $\\si$. Try to introduce regularization and minmize\n", "$$ \\umin{h} F(h) \\eqdef \\Ll(K h,y) + \\la R(h) $$\n", "where for instance $R=\\norm{\\cdot}_2^2$ or $R=\\norm{\\cdot}_1$." ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [], "source": [ "run -i nt_solutions/ml_3_classification/exo6" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [], "source": [ "## Insert your code here." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Multi-Classes Logistic Classification\n", "-------------------------------------\n", "The logistic classification method is extended to an arbitrary number\n", "$k$ of classes by considering a familly of weight vectors $ w_\\ell\n", "$_{\\ell=1}^k, which are conveniently stored as columns of matrix $W \\in \\RR^{p \\times k}$.\n", "\n", "\n", "This allows to model probabilitically the belonging of a point $x \\in \\RR^p $ to a\n", "the classes using an exponential model\n", " $$ h(x) = \\pa{ \\frac{ e^{-\\dotp{x}{w_\\ell}} }{ \\sum_m e^{-\\dotp{x}{w_m}} } }_\\ell $$\n", "This vector $h(x) \\in [0,1]^k $ describes the probability of $x$\n", "belonging to the different classes, and $ \\sum_\\ell h(x)_\\ell = 1 $.\n", "\n", "\n", "The computation of $w$ is obtained by solving a maximum likelihood\n", "estimator\n", " $$ \\umax{w \\in \\RR^k} \\frac{1}{n} \\sum_{i=1}^n \\log( h(x_i)_{y_i} ) $$\n", "where we recall that $y_i \\in \\{1,\\ldots,k\\}$ is the class index of\n", "point $x_i$.\n", "\n", "\n", "This is conveniently rewritten as\n", " $$ \\umin{w} \\sum_i \\text{LSE}( XW )_i - \\dotp{XW}{D} $$\n", "where $D \\in \\{0,1\\}^{n \\times k}$ is the binary class index matrices\n", " $$ D_{i,\\ell} = \\choice{\n", " 1 \\qifq y_i=\\ell, \\\\\n", " 0 \\quad \\text{otherwise}.\n", " }\n", " $$\n", "and LSE is the log-sum-exp operator\n", " $$ \\text{LSE}(S) = \\log\\pa{ \\sum_\\ell \\exp(S_{i,\\ell}) } \\in \\RR^n. $$" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [], "source": [ "def LSE0(S): return np.log( np.exp(S).sum(axis=1,keepdims=1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The computation of LSE is\n", "unstable for large value of $S_{i,\\ell}$ (numerical overflow, producing NaN), but this can be\n", "fixed by substracting the largest element in each row,\n", "since $ \\text{LSE}(S+a)=\\text{LSE}(S)+a $ if $a$ is constant along rows. This is\n", "the [celebrated LSE trick](https://en.wikipedia.org/wiki/LogSumExp)." ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [], "source": [ "def max2(S): return np.tile( S.max(axis=1,keepdims=1), (1,S.shape[1]) )\n", "def LSE(S): return LSE0( S-max2(S) ) + S.max(axis=1,keepdims=1)" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.0" ] }, "execution_count": 62, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# check equality of LSE and LSE0\n", "S = np.random.randn(4,5)\n", "np.linalg.norm( LSE(S)-LSE0(S) )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The gradient of the LSE operator is the\n", "\n", "$$ \\nabla \\text{LSE}(S) = \\text{SM}(S) \\eqdef\n", " \\pa{\n", " \\frac{\n", " e^{S_{i,\\ell}}\n", " }{\n", " \\sum_m e^{S_{i,m}}\n", " } } $$" ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [], "source": [ "def SM0(S): return np.exp(S) / np.tile( np.exp(S).sum(axis=1,keepdims=1), (1, S.shape[1]) );" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similarely to the LSE, it needs to be stabilized." ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [], "source": [ "def SM(S): return SM0(S-max2(S))" ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.6840225185876241e-16" ] }, "execution_count": 67, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Check equality of SM and SM0\n", "np.linalg.norm( SM(S)-SM0(S) )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We load a dataset of $n$ images of size $p = 8 \\times 8$, representing digits from 0\n", "to 9 (so there are $k=10$ classes).\n", "\n", "\n", "Load the dataset and randomly permute it.\n", "Separate the features $X$ from the data $y$ to predict information." ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [], "source": [ "from scipy import io\n", "name = 'digits';\n", "U = io.loadmat('nt_toolbox/data/ml-' + name)\n", "A = U['A']\n", "A = A[np.random.permutation(A.shape[0]),:]\n", "X = A[:,0:-1]\n", "y = A[:,-1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$n$ is the number of samples, $p$ is the dimensionality of the features, $k$\n", "the number of classes." ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [], "source": [ "[n,p] = X.shape\n", "p1 = int(np.sqrt(p))\n", "CL = np.unique(y) # list of classes.\n", "k = np.size(CL)" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPgAAAD8CAYAAABaQGkdAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQ5jAIUzgECZwCBM4hAkcwgQOYX8DUd9Jj0ugpkAAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f = X[1,:]\n", "f = np.reshape( f,(p1,p1) )\n", "plt.imshow(f.max()-f, cmap=\"gray\")\n", "plt.axis('off');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Display a few samples digits" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "q = 5\n", "plt.clf\n", "for i in np.arange(0,k):\n", " I = find(y==CL[i])\n", " for j in np.arange(0,q):\n", " f = X[I[j],:];\n", " f = np.reshape( f,(p1,p1) )\n", " plt.subplot(q,k, j*k+i+1 )\n", " plt.imshow(f.max()-f, cmap=\"gray\")\n", " plt.axis('off')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Perform dimensionality reduction using PCA. " ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# substract mean\n", "X1 = X-X.mean(axis=0)\n", "# covariance, not used\n", "C = X1.transpose().dot( X1 )\n", "# SVD, the V matrix contains the eigenvectors to project onto\n", "# WARNING: Matlab and Python do not have the same convention for the SVD. \n", "# For Python, it reads X1=U*diag(s)*V\n", "# For Matlab, it reads X1=U*diag(s)*transpose(V)\n", "U, s, V = np.linalg.svd(X1)\n", "Xr = X1.dot( V.transpose() )\n", "# display the decay of eigenvalues\n", "plt.plot(s);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Display in 2D." ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "data": { "image/png": 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LROF+kB/xF9u3+HX0n3QtpdP3t2+rvZ+Pm4pACoQytegNYNtIU+DKFLIMnp/2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\nAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "col = np.array( [ [1,0,0], [0,1,0], [0,0,1], [0,0,0], [0,1,1], [1,0,1], [1,1,0], [1,.5,.5], [.5,1,.5], [.5,.5,1] ] ).transpose()\n", "for i in np.arange(0,k):\n", " I = find(y==CL[i])\n", " plt.plot(Xr[I,0], Xr[I,1], '.', color=col[:,i])\n", "plt.axis('equal');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Display in 3D." ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [ { "data": { "image/png": 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LFPN14xEOhydE3ycDrigucSaLDPM9XmeqSNERw0gkwtq1a9myZcuSE0PHO3WmPsjF6FPM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\nXU1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from mpl_toolkits.mplot3d import Axes3D\n", "fig = plt.figure()\n", "ax = Axes3D(fig)\n", "plt.clf\n", "for i in np.arange(0,k):\n", " I = find(y==CL[i])\n", " ax.scatter(Xr[I,0], Xr[I,1], Xr[I,2], '.', color=col[:,i])\n", "plt.axis('tight');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compute the $D$ matrix." ] }, { "cell_type": "code", "execution_count": 81, "metadata": {}, "outputs": [], "source": [ "D = np.double( np.tile( CL, (n,1) ) == np.tile( y, (k,1) ).transpose() )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Dot product between two vectors." ] }, { "cell_type": "code", "execution_count": 82, "metadata": {}, "outputs": [], "source": [ "def dotp(x,y): return x.flatten().dot( y.flatten().transpose() )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define the energy $E(W)$." ] }, { "cell_type": "code", "execution_count": 83, "metadata": {}, "outputs": [], "source": [ "def E(W): return 1/n*( LSE(X.dot(W)).sum() - dotp(X.dot(W),D) )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define its gradients\n", " $$ \\nabla E(W) = \\frac{1}{n} X^\\top ( \\text{SM}(X W) - D ). $$" ] }, { "cell_type": "code", "execution_count": 84, "metadata": {}, "outputs": [], "source": [ "def nablaE(W): return 1/n * X.transpose().dot( SM(X.dot(W)) - D )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Exercise 7__\n", "\n", "Implement a gradient descent\n", "$$ W_{\\ell+1} = W_\\ell - \\tau_\\ell \\nabla E(W_\\ell). $$\n", "Monitor the energy decay." ] }, { "cell_type": "code", "execution_count": 86, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "run -i nt_solutions/ml_3_classification/exo7" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [], "source": [ "## Insert your code here." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generate a 2D grid of points over PCA space and map it to feature space." ] }, { "cell_type": "code", "execution_count": 87, "metadata": {}, "outputs": [], "source": [ "M = np.abs(Xr.flatten()).max()\n", "q = 201\n", "t = np.linspace(-M,M,num=q)\n", "[B,A] = np.meshgrid(t,t)\n", "G0 = np.vstack([A.flatten(), B.flatten()]).transpose()\n", "Xmean = np.tile( X.mean(axis=0,keepdims=1), (q**2,1) )\n", "G = G0.dot(V[0:2,:]) + Xmean" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Evaluate class probability associated to weight vectors on this grid." ] }, { "cell_type": "code", "execution_count": 88, "metadata": {}, "outputs": [], "source": [ "Theta = SM(G.dot(W))\n", "Theta = np.reshape(Theta, (q, q, k) )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Display each probablity map." ] }, { "cell_type": "code", "execution_count": 90, "metadata": {}, "outputs": [ { "data": { "image/png": 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gsipPmvd5RC4k+PztAleN0OGds+y1X0y1YubFipkXYi+qPbWlaNoo6tIZG2bW9JncbWTm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\nHiAquVdUVFQ8QPz/wVDrZ6pPW9MAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.clf\n", "for i in np.arange(0,k):\n", " plt.subplot(3,4,i+1)\n", " plt.imshow(Theta[:,:,i].transpose());\n", " plt.title('Class ' + str(i+1));\n", " plt.axis('off')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Build a single color image of this map." ] }, { "cell_type": "code", "execution_count": 91, "metadata": {}, "outputs": [], "source": [ "R = np.zeros((q,q,3))\n", "for i in np.arange(0,k):\n", " for a in np.arange(0,3):\n", " R[:,:,a] = R[:,:,a] + Theta[:,:,i] * col[a,i]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Display." ] }, { "cell_type": "code", "execution_count": 92, "metadata": {}, "outputs": [ { "data": { "image/png": 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d16pN8l3SKPKuG7eGd3D9dQwOK0kee8geX0nsc1cCh7WoF1Dt3swyhWAgFvFg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\nZUpRm1TLour3b0SLsn0vzA359GqbVekuPI5e1M2HPwTgEAFCgjkMsYBRC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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.clf\n", "plt.imshow(R.transpose((1, 0, 2)), origin=\"lower\", extent=[-M,M,-M,M])\n", "for i in np.arange(0,k):\n", " I = find(y==CL[i])\n", " plt.plot(Xr[I,0], Xr[I,1], '.', color=col[:,i])\n", "plt.axis('off');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Exercise 8__\n", "\n", "Separate the dataset into a training set and a testing set. Evaluate the classification performance\n", "and display the confusion matrix. You can try the impact of kernlization and regularization." ] }, { "cell_type": "code", "execution_count": 93, "metadata": {}, "outputs": [], "source": [ "run -i nt_solutions/ml_3_classification/exo8" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [], "source": [ "## Insert your code here." ] }, { "cell_type": "raw", "metadata": {}, "source": [ "" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "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": "3.7.1" } }, "nbformat": 4, "nbformat_minor": 1 }