{ "cells": [ { "cell_type": "code", "execution_count": 7, "id": "c05e06a0", "metadata": { "collapsed": true }, "outputs": [], "source": [ "import scipy,pylab,numpy\n", "from numpy import *\n", "from scipy import *\n", "from pylab import *\n", "from urllib import urlopen\n", "from gzip import GzipFile\n", "from scipy.spatial import distance\n", "from scipy.spatial.distance import cdist" ] }, { "cell_type": "markdown", "id": "86db21aa", "metadata": {}, "source": [ "Linear Classification Problem\n", "================\n", "\n", "Let's generate a linear problem, as before." ] }, { "cell_type": "code", "execution_count": 8, "id": "0b8f4b1a", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "608" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data = random_sample((1000,2))\n", "labels = (data[:,0]*0.7+data[:,1]*0.4>0.5)\n", "sum(labels)" ] }, { "cell_type": "code", "execution_count": 9, "id": "28c89b4a", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "392 608" ] }, { "data": { "image/png": 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3o3N8Lh/n5GDWbbehZvduoQzVQAl3Gc5KGmTRKbKEsqxCYl5BRckB88vAbDgt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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "d0 = data[labels==False]\n", "d1 = data[labels]\n", "figure(figsize=(6,6))\n", "plot(d0[:,0],d0[:,1],\"bo\")\n", "plot(d1[:,0],d1[:,1],\"ro\")\n", "print len(d0),len(d1)" ] }, { "cell_type": "code", "execution_count": 10, "id": "33797970", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 1. , 0.62170828, 0.20003034],\n", " [ 1. , 0.03303012, 0.36609942],\n", " [ 1. , 0.34112627, 0.96111128]])" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "augmented = concatenate([ones((len(data),1)),data],axis=1)\n", "augmented[:3,:]" ] }, { "cell_type": "markdown", "id": "e46e3264", "metadata": {}, "source": [ "Least Square Solution\n", "====================\n", "\n", "We now want to find a vector $a$ such that $a \\cdot x_i \\approx c_i$ for all $i$.\n", "\n", "We can write this as a matrix and vector equation if we put the measurements into the\n", "rows of a matrix $X = {x_1\\choose x_N}$ and $c = {c_1\\choose c_N}$\n", "\n", "$$X \\cdot a^T = c$$\n", "\n", "In order to solve this, we take the pseudo-inverse of $X$:\n", "\n", "$$a^T = X^\\dagger \\cdot c$$\n", "\n", "The pseudo-inverse is a generalization of the inverse matrix for non-rectangular and/or non-full-rank matrices." ] }, { "cell_type": "code", "execution_count": 21, "id": "b5b46453", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-0.345563974086 1.27003201537 0.600651460697" ] } ], "source": [ "a = dot(linalg.pinv(augmented),labels)\n", "d,a0,a1 = a\n", "print d,a0,a1" ] }, { "cell_type": "markdown", "id": "4fa2d76e", "metadata": {}, "source": [ "Note that the decision boundary is at $a\\cdot x = 0.5$, not at $a\\cdot x = 0$, since\n", "we want the decision boundary halfway between the two numerical values $0$ and $1$,\n", "corresponding to the labels." ] }, { "cell_type": "code", "execution_count": 24, "id": "b6cdcc9d", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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k3pjBK4x2tWqlRoyEzGttJiilOJ9THigtCkZkZ8TTD9gFRgy+Ey6cgJKsEtz9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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "d0 = data[labels<=0]\n", "d1 = data[labels>0]\n", "figure(figsize=(6,6)); xlim((0,1)); ylim((0,1))\n", "plot(d0[:,0],d0[:,1],\"bo\")\n", "plot(d1[:,0],d1[:,1],\"ro\")\n", "plot([0,-d/a0+0.5],[-d/a1+0.5,0],\"g\")" ] }, { "cell_type": "markdown", "id": "9e4b70c0", "metadata": {}, "source": [ "The problem with these kinds of least square solutions is that they are not very good: \n", "although a linear function can represent the decision function just fine,\n", "it is not a good approximation to the function represented by the labels.\n", "\n", "In fact, the function represented by the class labels is, effectively,\n", "the posterior probability distribution, a smooth function, that is in general\n", "better approximate by sigmoids (see below)." ] }, { "cell_type": "markdown", "id": "7872b261", "metadata": {}, "source": [ "Sigmoid Functions\n", "=================\n", "\n", "A problem with computing linear least square approximations to\n", "the class label is that we can already see that a linear approximation\n", "can never be very good: the class label is essentially a step function,\n", "but the linear approximant to grows without bounds.\n", "\n", "We've already seen that we can interpret the linear functions $g_c(x) = w_c \\cdot x$ \n", "as discriminant functions, but there is no reason to limit ourselves to linear functions.\n", "\n", "What we would really like to optimize (in the two-class case) is:\n", "\n", "$$\\hbox{err} = \\sum_i (H(w \\cdot x_i) - c_i)^2$$\n", "\n", "Here, $H(x) = \\left\\lfloor x > 0 \\right\\rfloor$, the Heaviside function. Unfortunately, we can't optimize that via gradient descent (the only non-linear optimization method that we know) because the Heaviside function does not have a derivative at 0.\n", "\n", "We can, however, compute the derivative of a continuous approximation of the Heaviside function, namely a sigmoid function.\n", "\n", "$$\\sigma_q(x) = \\frac{1}{1+e^{-q\\,x}}$$\n", "\n", "This function looks non-symetrical, but it actually is. Let's plot it:" ] }, { "cell_type": "code", "execution_count": 9, "id": "f2bd8e5b", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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bLUhIIKNpU8nIhVOwGMh37dpFYGAg/v7+uLu7M2rUKCIiIkq0mzdvHg899BBN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\nCCEcnARyIYRwcBLIhRDCwf0/nGc7tBQJt1kAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "xs = linspace(-6,6,100)\n", "def sig(x,q): return 1.0/(1.0+exp(-q*x))\n", "plt.cla()\n", "plot(xs,sig(xs,1.0))\n", "plot(xs,sig(xs,2.0))\n", "plot(xs,sig(xs,4.0))\n", "plot(xs,sig(xs,8.0))\n", "savefig(\"temp.png\")" ] }, { "cell_type": "markdown", "id": "13f33b8c", "metadata": {}, "source": [ "Using the sigmoid function, the discriminant functions become:\n", "\n", "$$g_c(x) = \\sigma(w_c \\cdot x)$$\n", "\n", "We don't bother introducing the scale factor $q$ because that is already contained in the weight vector $w_c$; that is, since the norm of that vector is not controlled and only the direction of the vector matters for the discriminant boundary, the gradient descent algorithm can itself let $q$ go to infinity in order to obtain better and better approximations to the Heaviside function.\n", "\n", "Using the sigmoid function, the discriminant functions become:\n", "\n", "$$g_c(x) = \\sigma(w_c \\cdot x)$$\n", "\n", "As before, we compute the gradient of the error:\n", "\n", "$$\\hbox{err} = \\sum_i (\\sigma(w\\cdot x_i)-c_i)^2$$\n", "\n", "Using the same sloppy notation for partial derivatives as before, we can write:\n", "\n", "$$\\frac{\\partial\\hbox{err}}{\\partial w} = 2 \\sum_i (\\sigma(w\\cdot x_i)-c_i) \\sigma'(w\\cdot x_i) x_i$$\n", "\n", "Note that\n", "\n", "$$\\sigma'(x) = \\sigma(x) (1-\\sigma(x))$$\n", "\n", "\n", "\n", "Let's implement this. Note that the class labels are zero and one again, $c\\in\\{0,1\\}$, matching the output of the sigmoid function $\\sigma(x) \\in [0,1]$." ] }, { "cell_type": "code", "execution_count": 11, "id": "266d24c5", "metadata": { "collapsed": true }, "outputs": [], "source": [ "def sigmoid(x): return 1.0/(1.0+exp(-x))" ] }, { "cell_type": "code", "execution_count": 12, "id": "ef88c29f", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 0.41829084, 0.31289947, 0.58718571])" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "w = random_sample((3))\n", "w" ] }, { "cell_type": "code", "execution_count": 13, "id": "87184a93", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 0.01 [ 0.41829084 0.31289947 0.58718571]\n", "100000 0.01 [-4.06342381 6.21008656 2.92048786]\n", "200000 0.01 [-5.49849138 8.13621486 4.09214148]\n", "300000 0.01 [-6.46527904 9.45443711 4.87551951]\n", "400000 0.01 [ -7.21890156 10.49123519 5.48224139]" ] } ], "source": [ "eta = 0.01\n", "for iter in range(500000):\n", " i = iter%len(data)\n", " if iter%100000==0: print iter,eta,w\n", " x = augmented[i]\n", " c = labels[i]\n", " s = sigmoid(dot(w,x))\n", " sprime = s*(1-s)\n", " delta = s-c\n", " w -= eta*(s-c)*sprime*x" ] }, { "cell_type": "code", "execution_count": 14, "id": "1a0c4b80", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "433 567" ] }, { "data": { "image/png": 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XXYbqXbuix4xIGUUrEUQrU2jKhYXJyfh2T/8iWc/uQ1YwM73KD95+EynTEy1J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PL8PaF/PKX9tIJZsi7sSdNyB+mbUNgTSezKLvp+eJ6hmgMhnzxX7lpJ7txwp+4xEwWtJexoYE0Q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\nAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "d,a0,a1 = w\n", "d0 = data[labels<=0]\n", "d1 = data[labels>0]\n", "figure(figsize=(6,6))\n", "ylim((0,1))\n", "xlim((0,1))\n", "plot(d0[:,0],d0[:,1],\"bo\")\n", "plot(d1[:,0],d1[:,1],\"ro\")\n", "plot([0,-d/a0],[-d/a1,0],\"g\")\n", "print len(d0),len(d1)" ] }, { "cell_type": "markdown", "id": "05ddf7b7", "metadata": {}, "source": [ "That looks quite good, but not perfect. Let's look at the value of the discriminant function." ] }, { "cell_type": "code", "execution_count": 15, "id": "343cc061", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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mD1JlXY45YvIfOfZR8O0fgJDdUUZfgM/xfzHzzTojZMu330oRaPTSwxUwBYuh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\n2re7zsiSWwC5qn17jXLRIDe+221maKnrUC29RbPCvbQA2MKXtCU5cmW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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "xs = linspace(0,1,100)[:,newaxis]\n", "ys = linspace(0,1,100)[newaxis,:]\n", "cla(); imshow(sigmoid(a0*xs+a1*ys+d).T,origin='lower'); savefig(\"temp.png\")" ] }, { "cell_type": "markdown", "id": "3d0571b5", "metadata": {}, "source": [ "Blue represents zero and red represents one. From this picture, we can see that the transition region between the two values is quite fuzzy; the decision boundary isn't at all sharp." ] }, { "cell_type": "code", "execution_count": 16, "id": "5462d9e3", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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PzzcMwzAOHDhg2Gw24/Dhw1aU63P79u3z6ILq1eSm12buWhN/gSdj8fLLL3P0\n6NGmPnNUVBSVlZVWlu0TnoxFuPBkLJKTkxk9ejSpqal06NCB3Nxc+vXrZ3Hl3ufJWLz44otMnDiR\ntLQ0zp07x8yZM+nRo4fFlXvfhAkTWLt2LXV1dcTGxlJQUEBjYyPQvtyMMIwQbXCKiIQx3YlJRCQE\nKdxFREKQwl1EJAQp3EVEQpDCXUQkBCncRURC0P8DzNazKRpule0AAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xs = linspace(0,1,100)\n", "ys = xs\n", "cla(); plot(xs,sigmoid(a0*xs+a1*ys+d)); savefig(\"temp.png\")" ] }, { "cell_type": "markdown", "id": "a914c733", "metadata": {}, "source": [ "Let's update a little longer and with a higher training rate." ] }, { "cell_type": "code", "execution_count": 17, "id": "701935b8", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 0.1 [ -7.84683128 11.35962138 5.98575717]\n", "100000 0.1 [-11.60182816 16.61438497 9.00802051]\n", "200000 0.1 [-13.81577983 19.70742599 10.76316596]\n", "300000 0.1 [-15.46759654 22.01714172 12.07428822]\n", "400000 0.1 [-16.81496314 23.90180674 13.14491147]" ] } ], "source": [ "eta = 0.1\n", "for iter in range(500000):\n", " i = iter%len(data)\n", " if iter%100000==0: print iter,eta,w\n", " x = augmented[i]\n", " c = labels[i]\n", " s = sigmoid(dot(w,x))\n", " sprime = s*(1-s)\n", " delta = s-c\n", " w -= eta*(s-c)*sprime*x" ] }, { "cell_type": "markdown", "id": "db01cc44", "metadata": {}, "source": [ "Now the decision boundary is a lot \"sharper\":" ] }, { "cell_type": "code", "execution_count": 20, "id": "c1302d55", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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L32bF2wQ2tub5pgGUFnjLrkvQKY0yllX1tlv1/W90S4yut12W3iTpdwrYRxL0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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "d,a0,a1 = w\n", "xs = linspace(0,1,100)[:,newaxis]\n", "ys = linspace(0,1,100)[newaxis,:]\n", "cla(); imshow(sigmoid(a0*xs+a1*ys+d))" ] }, { "cell_type": "code", "execution_count": 19, "id": "aa941c39", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "xs = linspace(0,1,100)\n", "ys = xs\n", "cla(); plot(xs,sigmoid(a0*xs+a1*ys+d))" ] }, { "cell_type": "markdown", "id": "5076058e", "metadata": {}, "source": [ "Let's do more of that still." ] }, { "cell_type": "code", "execution_count": 21, "id": "5a7388e3", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 1.0 [-17.9677928 25.51467577 14.06171267]\n", "100000 1.0 [-25.35304656 35.90923298 20.11625363]\n", "200000 1.0 [-30.01543776 42.40278885 23.80803724]\n", "300000 1.0 [-33.64150081 47.45434356 26.67869104]\n", "400000 1.0 [-36.69066627 51.70397516 29.09337889]" ] } ], "source": [ "eta = 1.0\n", "for iter in range(500000):\n", " i = iter%len(data)\n", " if iter%100000==0: print iter,eta,w\n", " x = augmented[i]\n", " c = labels[i]\n", " s = sigmoid(dot(w,x))\n", " sprime = s*(1-s)\n", " delta = s-c\n", " w -= eta*(s-c)*sprime*x" ] }, { "cell_type": "code", "execution_count": 22, "id": "4b70e197", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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6Z555hgsXLtBqtQC4dOkSFy9e5Mknn+Tpp5/m0qVLXLp06VgfVKPiFOHh6siu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\nuvZFk2Jkgs4a5+zyg9e6a19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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "d,a0,a1 = w\n", "xs = linspace(0,1,100)[:,newaxis]\n", "ys = linspace(0,1,100)[newaxis,:]\n", "cla(); imshow(sigmoid(a0*xs+a1*ys+d))" ] }, { "cell_type": "code", "execution_count": 23, "id": "436f74c5", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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4A9GJuHLv6uqS1+sdfOzxeNTa2jrm8Rs3btTq1atH/V5dXd3g16WlpSotLZ3YpIDCe+5s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\n2ND/A3a750TUfWHaAAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xs = linspace(0,1,100)\n", "ys = xs\n", "cla(); plot(xs,sigmoid(a0*xs+a1*ys+d)); savefig(\"temp.png\")" ] }, { "cell_type": "markdown", "id": "b9703b3c", "metadata": {}, "source": [ "Using scikit-learn\n", "==================" ] }, { "cell_type": "code", "execution_count": 24, "id": "4199512d", "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sklearn import linear_model,datasets" ] }, { "cell_type": "code", "execution_count": 25, "id": "4fbd89c4", "metadata": { "collapsed": true }, "outputs": [], "source": [ "logreg = linear_model.LogisticRegression(C=1e5)" ] }, { "cell_type": "code", "execution_count": 26, "id": "badcc5f6", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "LogisticRegression(C=100000.0, dual=False, fit_intercept=True,\n", " intercept_scaling=1, penalty='l2', scale_C=False, tol=0.0001)" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "logreg.fit(data,labels)" ] }, { "cell_type": "code", "execution_count": 32, "id": "923a1bdf", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1 1 1 1 0 0 1 1 0 1]\n", "[1 1 1 1 0 0 1 1 0 1]\n", "errors 0" ] } ], "source": [ "z = logreg.predict(data)\n", "print 1*labels[:10]\n", "print z[:10]\n", "print \"errors\",sum(z!=labels)" ] }, { "cell_type": "code", "execution_count": null, "id": "1a8e0936", "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": {}, "nbformat": 4, "nbformat_minor": 5 }