{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\"Open\n", "\n", "\n", "# TP Descente de gradient stochastique" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from TP_gradient_stochastique import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Régression en faible dimension" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On se propose d'illustrer le principe du gradient stochastique sur un exemple très simple de régression linéaire en une dimension. On observe des couples $(x_i,y_i)$ réalisations de $(X,Y)$ avec $X$ qui suit une loi uniforme sur $[0,1]$ et \n", "$$Y = aX+b+\\epsilon$$ \n", "où $\\epsilon \\sim \\mathcal{N}(0,1)$. \n", "On commence par tirer aléatoirement les observations $(x_i,y_i)$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "M = int(1e3)\n", "x = np.random.rand(M,1)\n", "sigma = 0.1\n", "y = x + 1 + sigma*np.random.randn(x.shape[0],x.shape[1])\n", "plt.plot(x,y,'+')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Descente de gradient\n", "\n", "On suppose maintenant qu'on observe les $(x_i,y_i)$ mais qu'on ne connaît pas $a$ et $b$. Pour déterminer $a$ et $b$, on propose de minimiser \n", "$$f(a,b) = \\frac 1 N \\sum_{i=1}^N (y_i - a x_i -b)^2$$\n", "\n", "La minimisation a évidemment une solution explicite, mais le but ici est d'illustrer l'algorithme de gradient stochastique. A titre de référence, on commence donc par effectuer une descente de gradient classique (déterministe) sur $f$, dont les étapes sont : \n", "$$a^{(k+1)} = a^{(k)} - \\rho\\frac 2 N \\sum_{i=1}^N x_i ( a^{(k)} x_i +b^{(k)} - y_i)$$\n", "$$b^{(k+1)} = b^{(k)} - \\rho\\frac 2 N \\sum_{i=1}^N ( a^{(k)} x_i +b^{(k)}-y_i)$$\n", "avec $\\rho$ le pas de la descente.\n", "Comme $f$ est strictement convexe, on sait qu'une descente de gradient classique avec un pas choisi suffisamment petit (inférieur à $\\frac 2 L$ avec $L$ la constante de Lipschitz du gradient de $f$) va converger vers la solution (voir par exemple [ici](http://users.ece.utexas.edu/~cmcaram/EE381V_2012F/Lecture_4_Scribe_Notes.final.pdf)).\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "f = lambda a,b : 1/(x.shape[0])*np.sum((a*x+b-y)**2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On se propose de faire $30$ expériences pour tester différentes initialisations." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "L = 30 # nombre d'experiences\n", "a0,b0 = 1+np.random.randn(L,),1+np.random.randn(L,) # initialisations\n", "niter = int(1e3) # nombre d'iterations de la descente\n", "rho = 0.1 # pas" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(15,6))\n", "t_a = np.zeros((niter,))\n", "cout = np.zeros((niter,))\n", "axes = plt.subplot(1, 2, 1)\n", "axes2 = plt.subplot(1, 2, 2)\n", "\n", "# Descente de gradient classique\n", "for l in range(L):\n", " a,b = a0[l],b0[l]\n", " for k in range(niter):\n", " t_a[k] = a \n", " dfa, dfb = 2/M*np.sum(x*(a*x+b-y)), 2/M*np.sum((a*x+b-y))\n", " a = a - rho*dfa\n", " b = b - rho*dfb\n", " cout[k] = f(a,b)\n", " axes.plot(t_a)\n", " axes.set_title('valeur de a au cours des itérations, pour 30 initialisations différentes')\n", " axes2.plot(np.log(cout))\n", " axes2.set_title('log(f(a,b)) au cours des itérations, pour 30 initialisations différentes')\n", "plt.show() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Descente de gradient stochastique\n", "\n", "On se propose maintenant de faire la même expérience avec une descente de gradient stochastique. A chaque pas on ne tient compte que d'un couple $(x_i,y_i)$. A l'étape $k$, on tire donc un $i_k$ uniformément dans $\\{1,\\dots,M\\}$ et on calcule\n", "$$a^{(k+1)} = a^{(k)} - 2\\rho_k x_{i_k} ( a^{(k)} x_{i_k} +b^{(k)}-y_{i_k})$$\n", "$$b^{(k+1)} = b^{(k)} - 2\\rho_k ( a^{(k)} x_{i_k} +b^{(k)}-y_{i_k})$$\n", "Les résulats de convergence pour le gradient stochastique nécessitent généralement que la suite de pas positifs $(\\rho_k)_k$ soit telle que la série $\\sum_k\\rho_k$ diverge et que la série $\\sum_k\\rho_k^2$ converge. Il est ainsi classique de choisir \n", "$$\\rho_k = \\frac{\\alpha}{\\beta k +1}.$$\n", "Dans ce TP on choisira généralement $\\beta = 0.01$. On prend ici $\\alpha = 1$.\n", "\n", "

Implémentez un gradient stochastique pour calculer le minimum de la fonction f précédente.

" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "exo1(x,y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## SGD pour la classification \n", "\n", "Afin de tester la descente de gradient stochastique en plus grande dimension, on s'intéresse à un problème de classification supervisée. \n", "Etant donné une base d'apprentissage constituée de $M$ vecteurs d'observations $\\{x^{(m)}\\}_{m=1,\\dots,M}$ vivant dans $\\mathbb{R}^p$ et de leurs classes $\\{y^{(m)}\\}_{m=1,\\dots,M}$ (on suppose ici qu'il y a deux classes $C_0$ et $C_1$, donc que les $y^{(m)}$ appartiennent à $\\{0,1\\}$), le but est de pouvoir classer n'importe quel nouveau vecteur de données dans une des deux classes $\\mathcal C_k$, $k=0,1$. \n", "\n", "\n", "Par souci de simplicité, on se restreint à des modèles linéaires pour la classification, qui peuvent s'écrire de manière générale sous la forme \n", "$$y(x;w) = f\\left( \\sum_{i=0}^{p-1} w_ix_i + w_{p}\\right)$$ \n", "avec $x = (x_0,\\dots,x_{p-1})$\n", "et $f$ est une *fonction d'activation* non linéaire fixée qui sera seuillée pour trouver les classes. Pour simplifier les notations, on écrit plutôt $x = (x_0,\\dots,x_{p-1},1)$ et $w = (w_0,\\dots,w_{p})$, et le modèle devient\n", "$$y(x;w) = f\\left( w^T x \\right).$$\n", "\n", "On choisit ici pour $f$ la fonction logistique $$f(x) = \\frac 1 {1+e^{-x}}.$$ \n", "\n", "Pour une donnée $x^{(m)}$, $f(w^T x^{(m)})$ représentera la probabilité que cette donnée soit dans la classe $C_1$. \n", "Pour trouver les paramètres $w=(w_0,\\dots,w_p)$ permettant de faire coller le modèle $y(x;w)$ le mieux possible avec les données observées $(x^{(1)},y^{(1)}),\\dots (x^{(m)},y^{(m)})$, on propose de maximiser la vraisemblance des données\n", "$$\\prod_{m=1}^M f\\left( w^T x^{(m)} \\right)^{y^{(m)}}(1-f\\left( w^T x^{(m)} \\right))^{(1-y^{(m)})}.$$\n", "\n", "\n", "\n", "donc de minimiser la fonction de perte\n", "$$\\mathcal{L}(w) = -\\frac 1 M \\sum_{m=1}^M y^{(m)}\\log f\\left( w^T x^{(m)} \\right) + (1-y^{(m)})\\log (1-f\\left( w^T x^{(m)} \\right)).$$\n", "\n", "1. Calculer le gradient de $\\mathcal{L}$ par rapport à $w$. \n", "2. Proposer et implémenter un algorithme de gradient classique et un algorithme de gradient stochastique pour résoudre numériquement le problème de minimisation \n", "$$\\min_w \\mathcal{L}(w).$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On commence par créer des données de faible dimension, que l'on crée à partir de tirages gaussiens." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "M = 1000 # nombre d'echantillons\n", "p = 2 # dimension\n", "omega = np.ones((1,2))*3\n", "n1 = int(M/2)\n", "X = np.vstack(( np.random.randn(n1,p), np.random.randn(n1,p)+np.ones([n1,1])*omega ))\n", "y = np.vstack(( np.ones([n1,1]), np.zeros([n1,1]) ))" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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eKijiSdr0LFPOfB87Dr5nDlFzPgtW7uSnq3ZyzcVnh/fyfc0LG/Ywdcwwpo8dHvv5bCZu93PXCIRectf9AsahsvvISRas3MkDizdyqi3em2X/8RaeXd0UE/GMouBz2c/eV1IZ4nCpHCLkQr+k3Pa0eV8zdsSQ9MPSwCEyZfTpfOkjUwAcT7ghr2HJpn2hP9wHfvO2OVy9NdFb5TOzJwCEKZvpY4fHUiXFyPuwcNVOlFJhEy2XpVv2x54eMgr+5+99IGZfhL6XyhCHS+UQIReqkvYiy1Ii4Yp8JuOx68jJWO46+bNAWBFqe564aMAtytSYkW2/dgYrAzQdPhHrPz4oo/jezdPZuPsoW/cdp66hmRSdDp4q7P8YPBV1Q3SrUxUmEk+KuP0MoS2zRPFUTyIOl8ogQi5UDe5YNHdIcXJ0W1pTKhcr1HYwg62GTNr90ipCazKKXF6XjKDBiG/TkVOx15YF4+IsbXnNxt1HYxbHclDAtRefza/fPhBuRr7WRtAVDBuc/p/1yKGDQvH3tfm6r0XpQucQIReqgmSnQevMSJbllytKdgBDztclp/08vGRrakXo8ZNtsWZb5aAhHBQBkPFgw66jHRJxgExGMXrY4NA5M3LoIP560XpzDw3/+usdTBx1ekFU3nyiNdZFsflEa9EoPUlfyq0LhYiQC1WBKzgQ9eN2898ddUEUK+9/dnUTB4+3sHTL/rBBlaeIVYQ+8tq2ot0Hi4lyNqN44ObpLN2ynx0H3qX+8AnW7zoaCqvnBQeeOrqWUjBiaA3N77WF3nDta55atTPWfiCfeER4YcOeAiGfO2UUg2vin/fljXsLonRLOU9AQt9AhFzo89Q1NMc81jVBqXyySrOjLoi0XPidjy0PJ9lbPEyBz33XXlhwr2Q0nRTxi8cMY/Pe44DJZe889B6/fvtA7OcUMHHUUC6dMIJfrtsdu5bWcPi9tvB9NqK3HRofXrKVaeecEcuZQ7zhVrHPu2XvcR5btiP2HuvuST4B+br4k4vQ+4iQC32StGgwm/G4fc6EgpFplvZcEGnpATeP/shr22LdBy3ZoMAneTA4/565fPM/11J/6ETqZ8h4KmZ7BHhx496CDoYaaDh0ouh1LErBPR85lyeW14dPHsvePsiytw8GPVaMRfJLV56betjpfl7rlU8ertqIPPYEFDT1UkUKq4TeR4Rc6BqNq6B+GUyeBxPmVOSSxaLBfN5nXMIqmKTYAWex/HlyVFsmOMx0+fSs8UVz8Pd+9Dy+87P16YvROizcsZw1bDBNR06GvceDYtCCSF4BH5ps7hkuR8Oxlhy3zRzPhl1H+V3TUZxv4QG/f9m4VNthcgNL88orYMPuozzy2jZGDh0Ue7px8/F20pFE5X0HEXKh8zSugh/fDPlWyAyCL/yiImLeHdFgsbFrSWH+g9kTWLByZ/hzWU+FszZX7DgUpkRa23yeXd3EuBFD+L1Lx7Jk8z7ebcmHP+cpCg5CFVDb0BwbRqEwrWh9P+6E0cDvdh3ly/Om8Phv3iEXpFN++mYjWusCB43Jp6tYjhuKb2DJ1JDCDKZ4uraRXN70Rr9m6lmMHjY4fAJyh2rUZL1weIbQ+4iQC52nfpkRcZ03f9Yvq4iQJ3Pdaflwl3IcFXOnjCKbibzjySZVLcGIt+ljh0f9TjzFPR85lxU7DrFl73HWNR6JqjCBhSt3ph5sZhR8ed6UAleLzXkrzAZhD2vvv2kaG3cf5alVO2Pvb23zOdaSY+bEEawKyvWt4yWX97nTcdDYIRIPLN4YDmBOum7c/LabhrKj5NY1HgkLnnJ5zUub9jHIacPrDtWwrQFEyPsGIuRC55k8z0TiNiKfPK8il+1IxV+HfNA2lRD8acXd5qx/+uZOPM94sj0FMyeO4Idv1JPL+0ULddLwPMWOg+8x7LQsR07mCr6f8cxQB3dz+s7P1hdaGRU8UxeJp4uvYdrY4dx1+UQeeW1bwWEkECs+sq4b94kmmYZKSxG15nwWrjQ++3kXnFnW5xd6HhFyofNMmGPSKRXOkUP5FX/lWg6tZ9xGtbYJ1adnjQ9TKXkf8n50ELmqvrlTa28Lotk0FHDNRWeFUTOYzejp2saC904ZfTo7gta3SawPHNLdOm70DPCBccO5/UMTU/PbdQ3NPPr6dnYcfI+MkxKyVkrr1z9r2GAGBePoajJRyknofUTIha4xYU5FBbyjlGs5LPY+t7GVhjDv7EabpbzhHUUDSzbv49dvHwifHkwv8/gdMgq+9JEpoWMHDWNHnMbeY6fQOh5dJ9MkK3Yc4sDx+CHr2WecluoFr2to5vbHlsfu/4lLzubqqWexcfdRnq5tDC2ft84cz60zx0thUB9EhFyoatK84Ha+ZnKU2/03TQvnYdrvNZ9oDT3YnooaWz1T10Q+78em7rywYQ/L3j4Yu789rExrZlWM5NPD3CmjqHGadCngUzPG0nyiNRyinAscMPd8ZArDhtSkfj4g1tUxm1Hkg+h59LDBqU8uaZvIqbZ86HxJE24R8L6HCLlQ9ZSar2nz0EAYkb5ZfzhMbSQjdevQuC0hYHUNzWzcfbQg9XDX5RPREHO6tEeyT/isSSNZ+OW5PPr6dl7ZvI+8hp+v3R1WdobNsXzN4795hwdumZ6aIkl2dbx9zkTGOQOmn0tMNQLzpJLxiFWGusVEbopLyvT7LiLkQpxu8IX3FLG+IW1+UPBiJuzcOnN8u+4NV7Tdr+3kHV9rlDJCjIbBNV7YqvY/32yM9QN3sXZD02vFpHNu/5CJeN2nhxkTRrBkc5RbTzQ8BIyYu5/LPdwttilZih0gZzyPvO+jFHxl3pTUYiJprtW3ESEXIrrJF95TuEKmEmXlCorm0t2o0xXtbMbjqgvPZMmmfZHHOxDWjKe4+4rJoTA+cMv0ggk9AONGnMaB4y3kfI2nFErB+l1H2bzHTCDK5XXoyU6OckvDpIHSy+Xbc/ukHSDHZo0Cw4bUpN63nENlidh7DxFyIaKbfOE9RfLQz51Qf+vM8WGe282Ru9iydSvGrTm/qPsk72v+7TfvoIOCpWnnnME9HzmXYy25ML9ek/W4aupZLFy1E1+DCsJrDbF+LtaTPW3scKaePYyzzziNIydaC1wznoKbZ4wNy/zTCoA62t+7q4fF7u9OIvbeQ4RciOgmX3iPEKSEZk2ex6yrzeaTnC6fliN3sRbFcrEHnHY827qmo/zt73+A6c6GMXXMMJ4NctOep1J7uQC8ve8488M8+1G++tEprG06GvwcEHRFfHHj3ugANEizAEV7q3R2AEdaX/dS0b7M3+xdRMiFiG70hXcrRVJCyYZY7QnN2/uOl7xNTcaU0pfqQf7Pr2zl8Hut5HzNm/WHmX/P3FAAdx05mVoNmlFw+ERb7LWNe46x8MuFP9fa5rNxz7GowjMQ87SNKdmz5oFbpqcKfjKKLxZdl4r2Zf5m7+K1/xZhQDFhDsz7ZvWIOKSnhBJYocmkVDiCEa9fOC1kk8yZPJLPzJ7Axy8+O3xNAeefeXrsfXuPtdCa12HZ/8NLtgLwtavP57aZ4xlc44X/0dlS/U/NGMv2/e/GrmPTP1+7+nymjx0eaw3Q0pYPZ4SCeTJ4eMlW6hriqRg3SraCn3xPGsX60pTCRux/ft1USav0AhKRC9XP5Hn4Xg3kAa8GLyUlVE5qIOkQARhzxmB+79JxPLG8ntqG5piAagiHMj/26+00HDpR0J522dsHWb79UBgNuzn8jbuPcuB4C4vW7o793LgRpzF1zDDAbDA/fTNubVxV30w2o8ho8INqVTvwOelisd0jIapobU9kOxtddzQ/L1QOEXKhcnSHdbGMay7YPYafnfo2c9Qm6vLT+Ev/AmalvK+91MDgmvigiNNqPB757KxYhOqKvacIfepXnj+a3Ucaw4lCLmnpj2dXNxXto7LryCk++/gK7r9pGg8s3siptsL36MAn3nj4BL8JZoGmuVju+ci5/OuvzfAIDQWHo2l0pNeN0DcQIR/IVFJ4u8O6WMY1I6fJBbzJBXiK1NmbaaKUfD3ZDdB9v7UFKgXKU+igbH3k0EFha9dsRvGJS85m6Zb94SxQi691rHVue3M623I+P31zZ6qIg2lZO33scKaPHc7y7Yfw/fQ2v8dboqZdduMp9TuxSHRdXYiQD1QqLbzrFkLuFKArZ10sww5p5lVGkugpFc7eLDVvstSBnm0i9dLGvdz+oYncdflE7r5iMo8t24GvoUYpPh1MKnKbU7XlNWcOG8zCe69gxY5D4YBmX5tcuNs6N03EPWXK/XXQQnfD7mOpvxaF2Ri+94sNEKROPE9x/03TCjYqtxlXNhPNJRWrYP9ChHygUknPeOMqWPMkYbWMl62MdbEMO6RNibS2GXvfA7dMB2h33mQxu1xdQzN3PLY8tAmua1rPzkPvBf2+zT1zzqSiZ1c3xdaz/3hLzPL4wzfq8XN+MAoofdanAj44fjjTxw1n2tjhNJ9oZfeRk0XL/m3Fp/GiRzOCfvrmTjbsPhpWdK7YcShmd/zYhWeyYschdh85KVbBfoYI+UClkp7x+mXg2+k4Ci67qzI58mJ2SCclNGvSnIKmWQ8v2RqmJLQ20W1ywlCxA72k+IHxbqdF/QC3zRzPM7UmN57x4PWtB3hl8z48pbjmorPI5Y1g5/N+2Dp3/j1zeW51Ez99cyd535Ttb957nPW7joYRMsDTRXLobr+X4DeOrwm97M/UNrLw3isYOXRQLPJ/bct+Xtm8L2io5YVFS2IVrH5EyAcqlfSMJzeFGXd1/BrF8vXJNrlpKSEuAGDL3uM8sHgjLU5eWWMGFic7BhY70Js7ZRQ1mXjhzvXTxvDDN8zAYzsUwr2OTaXsPnIyrOL0tWbJ5n1kM54pgVeKdY1HqGtoDn/26bqmoP+5CodX2Aj5a1efz8IvG8F353N6wPRxw1nXdBQwIj5p1NDY4Oa2fJSPt50dFZAPDmLb8pprLzkLBew7doote49LRF7liJAPZCrVS7yrm0JH8vWJlNCutS/x2VWHwjRK3o+7Rjxl+od87erzCy6VdqA3a9JInrr3CjNo4cC7TDnzfUwcdTpojcJEw9YaCPFDQ4Cn3mwMrS2+hhnjh7O6oZm8b4ZNLN16ICz0sdG69gvnktrr2h7gn308mpV5xZRRoZBr4hsNmMIlux771JHJePi+T9DanFff2h8+ZaxrMpOBilWHCn0fEXLB0FUHS6lNob1rdyRfn4j+l+cviQY1Y9IodpCxp4yQuamDcho7zZo0kq987Dw++/gKth94jyWb9zn5cVN8c9+1FwKFw5s/ftFZsf4s0doMNuIuNZd0y97j3L9oA3lfM7jGfO+jF5zJvmOnuP1DE2k+0RoOu7CNrr73qWn89M2dnHXGaXz1Y+eFn8196nhudRMLggrRZP/0FzbsESGvYros5EqpCcBPgDGYwrPHtNbf7+p1hR6kO7setnftxlVwtNEckPq0n6+fMIe3/q8nad70KiMvuYZzz5rFoLoVBYKYZiHsiFtjxY5D4YGk9Y4rzBJ/u80U37itcVvafJ5d3cRVU+NCPjjrkfHApro9zzS6ShuI8dzqJv719e2xaPlUm893f74+XMPmPRv43s3TqQk2gWxggbTOnOze45w5bDAQPXG4n7FY3xe3B7lQfVQiIs8B39Rar1ZKDQPqlFIva603VeDaQk/QnV0P3WvnTsG6BfFDyyduMt/3sjDrCzDjzqL3rmtoDgpp2sjlr2TQtjbm31Okz7Z9CvDmAeZ6HWnsNHLoIJSKi/ikUUPZefhErDVu1lO0Brnn/6xthNnx0XC2CnPO5BHUNTTj+/FJ97bf+V8HEXgabhFSW16zYffR2CDppVv2h5uOOyw5uVElN48te4+Hzb0kGq9uuizkWus9wJ7g78eVUpuBcYAIebXQnV0PJ88DLwP5PKBhzQJzGDphjvGe54PZkn7QNKqEiCcLadyDwZggF3kKKLf0vK6hmQcWbwxTIgozROLej55X0Br3wPGWMALP5TVrGppjG4B9vSXwjicrMG1BU5qI24NKl5qMQkE4SDrna17ZvK+gNUCxjcqN0GdNGhl2iHQPYYXqo6I5cqXUZOAyYGXK9+4F7gWYOFF2/x6h3Lx3d3Y9nDAHLrgO3lpsvs63OlF5UryK1zomC2mS49JipDxh1PkXsGLHoVguOm0akHsvMDnoKy8YzX3XXhgK37Ormzh4vKXAQw7GRpjGe615ssFsz6TdsVgkHvYeb/NRnmLmxBFcePYwpo0dHhugYX9eQdgLxr1HqcpWKQzqH1RMyJVS7wOeBe7TWheUpGmtHwMeA5g9e3b5TZ+FztHRvHc5DpbkxlDORtG4Ct5+2XnBicpn3AWr/wP8nEmtlLAtutG0HYh8qx1lllxH4gnjrdNmpApWMSFLRu5WxC1PB75xgKxnouRc3nj83EhcBTkWDWzf/y41WY/b50xg+tjhoT1w5NBBZLxCtw0Ykf/oBWcyethgpo8dzgOLN1LX0BybR5ocoJG2URUTa+kh3n+oiJArpWowIj5fa/1cJa4pdJFK572TG8P1D8KL3yp9iFm/DI42GaF28XOR8KoMkA/+LE7RRk7FNiznCeOVbe+nNbel7OrOZN8Vd9Dxo69vjx0S5ny46/IJjBsxhOMn28IGVQC3zBjLofdaw6ZWdqRaeDDpqbDEPuMpbvrgOfx8bdRKd++xFvZu2segrGl8667VinXaU4alrqGZh5dsLSrW0kO8/1AJ14oC/h3YrLX+x64vSagI5eS9O2I5TG4MmxcV3yisuOZaCLpMBaGqD6hoPfXLApHXkbiXWEdqI6fYYWoLLP07uOrbsSeMuX5zqmCVEjJ7HzeavfuKybycMvpt+tjhscPCx5btQAfTfK6fNibqJa7h4PGWSFiDEnsNKDSnD85y3SVn87umI+w91hJery3ns+qdw2B+e2QyxqlSKi2SPFNIS0VJl8P+QyUi8iuBzwPrlVJrg9e+o7V+vgLXFjpLe3nvjqZekhvDxbdAw/L0jaJ+mRFV/KgxiFKglTn4vP7B6F5dPWS167L327HUrMv5PMUEqyPjy1rbfCPQidsroo6CEA0vtg4Sd1iFAkYPGxxLEaEU+byxAz4VVIXWZBQZD4IAHg1scwZP+FqzcffRkmmRgjMFRUFTLfs7EAGvfirhWvkN5t9Roa9RKu/d0dRL2sZw9iXpG8XkeYFw2xdsI+/gz5OHil+zPZJPEfYaS//OiLj2Uz9PMcEqd3yZe6jokvFg95GToeuj1M9kPMVtM8dz28zxBf7xp1btDPuntOZ1+B+Ua2W02FL7bMYLPeG7nDXYtbtDJdDxDUfoX0hlZ1+mOwY1WDpjOXQ3Bru2IaOi0Wr2AHTdwvjPeVkj7H6+8F4daRNQ7CliwhyTTin2hNBJ3Ig9mf+21sCcD/NX7uTpoFFVMr9u8+EqaKJlr5ss0knuEe6XySZZNVmP6WOH80xtY9g75alVce/4rEkjeeCW6aE/PVskB15OpavQ9xEh76t0Z7UldM1yGK6txUTAeJAdHB2A2r7kACg454Nw2R+aSLwj90puZKWeIrrJQmlF8ZHXtoXRsYKCsXCteR3aEV1hnDpmmIm439zJS5v28eqW/Txw8/TwcBLgmbqmmK0Sot+ebdK1YfdRDh5v4cxhg7k1iOhzjvon52vajSSjzAS8fN4vaI4l9sP+gwh5X6U7qy0taRF2hw4+bZdB3zkAbSEeT2rYtQb2bSpvM3IjfeuK8TJw2edgzIzSTxEVaAJWLEK1fc/d3HZbYkDEweMt3Bn0Mq/JqDBCf/T17WG+O5fX/NXP1kPQB+a2meNDN4sCzjvzdBoOnyCX12F/9WJVl3Zqke0rYycWub3YrdjnNQXj5sq1H0rU3vcRIe+rVNp1UopOH3w6EXlmEIz5IGx/NfHmoENJsjy/vXUoBb5vfjafh9ofmnvc8A8dj+zLZMHKnbFmVW6EmtYb5dnVTTxd20gub4p8NHbYQxShz5o0kh0H34vdxwcIxFNjyvztrM/tB96LovFEp0WXYqPpXHEGHasOzfua54I1QXn2Q4naqwMR8r5KpV0npejKweeQUZGw2lx5iLUeppTnF1tH6HYJHC6+M1gh3wp718JND5f+PI2rzKaBKtm7JXxv/TLeOm0G9y9qDSPY1rbCCNWNZOdOGcXf/v4HYgeXzyUqPW2aZMro02OuEw+zT9VkPc4YnCWv3Tk/EW6nxVIHtTZihkJxvvuKyfzbb94JC46erm0MC6nKsR9K0VB1IELel+mK66Qj0XpXDz5dMoOj/imZmqA8/1cYr3ibSZecMyNdYIeMIohXzfuv+DpsfQEObHHe1I5BqnEVPPFJ81kA1syHuxenr9XZDM9TWWbwbeq4EDBdCt2+4DZaLTbn0/J0XVOsFwvAVz52Hq9u2U8ur8lmVJgjHzl0UEGfFTcP73ZaTIuEoyZiTeTypsDoM7MnFBQIHWvJsdBpX+uKcXv2Qykaqg5EyKuVUuLbmfL8zhwUplkB714cuFZ0VHK/7ZUoDbOrzvxjBRaia5w8FETwvvmz5Sgcfie6n1djNoBS1C+DfFv0daknDGczzAJXZt9iTduFeKpw9uegQJhLRaezJo0Mh0Yk/eo/DaYIua8/8tq2yB6IOdi85qJocs/6XUeL3iutiVhrXrNg5c6wh7mN0u2Q6M6IsRQNVQci5NVKKfHtzEFpe4MhXHG2NsMnPmlEM1MDd/8qukbyOtbn7ebP863mmmsXRgeaF1wXVYF6WUDFZ4HO/FyZTxc1UURe6gljyKjA7+6hMoO48cbPMPjdyaFgPfLatphwK2BOdhuz9Ebq1DTmTvlwwSWTEa4b0SenFNlo1x5M3vORc3liuZn0k814qU22LMmCH4stRLp/0QZ8rYtG6R2ho0VDcjja84iQVzPFxLeSB6WNq+BHN0T9UtbMN6K9bkEklrGOhg61Txgny5gPwsjJpp+KDoQ5MwjQzoaTjzokosw/Y2YELXB9I87lzAKdMMcciK75CQw7B678hnl92UOFA5xf/JaJ/j0Prn+Qi2Zfy0X2e8uW8fH3zeBfnLTC58fv48INfxv8XhfheVdge52nkTwoTIppMtp189H5vM8dcyYydsSQVEFMNhG7aupZLN16gHw+KkSyh682Su+Jg0o5HO0dRMj7G1agr3+wuLujI6mX334/3vQq32Yi6T2/S7xRxe9/6hj89mHzWtLJojJww9+bytC1TyV85xD2Xtm7Nrpuqdy4uymB08xrE5z/ifTmXjELpYqqTZ3fzUWZQfz85id5JYjSL1r/N5G90m9r90nHFeaWNp+/+rmZjZnMr7tC5+ajw+6OKaSlPBas3MkLG/Yw7ZwzeGJ5fTThiJ47qJTD0d5BhLw/Ua5AdyT1cnxP4gUNq3/iiHvQBGvGnfH7az95pTh71xrxvP5B8/c1C6JDUntNVNRUq1jUn/zMl95RvLlX7qTZXK68r/h4ucTv5qJT67jo6mvNfdYsINxwvEy7h8Ju6sS3XQowop7mRuloPtrdBOwwjNacz5v1h7n/pmls2H2UZ+qayOd77qBSDkd7BxHy/kS5At0Rl8plf2gOJy1jPgB710dfj5sZNcFa9lB0/6KYlqysftKIvd1wBg+PIng0XP4VuOiTsObJwulC9rNay6P7me0m4Db3eufXUcD/1q9g60sm964UTL3BpF/s78n93XhZI/iNq9i19iXOybcFq1emQKmdfL0V5oeXbGXZ2wfD1zXF3SidbWKVjISbT7QW2COL5e4rGTHL4WjvIELenyhXoDviUpl9t/lz8yIjinvXxYX8nBnFRdDPGYFVGZh6PZw8AjtXGAG3Yp87ZVI1zfXx+27+hfnz9NFwbLf5u5+LH5DavujuZ55xp/nH/WxrfhLfjOxYOQ1sfTHKo7u/m3ULzSZS9xP8NQv519bP8R0vSw05vOwgtp79SV55bVu7YjVr0kjuu/ZC3qw/TGubHw6fqHTqIS0S7q3JQNJRsedROtk0ogeYPXu2rq2t7fH7Dgg6Wu3ZmffbgcmZQYUWwrS/23L7glx4QGYQzP1jJyJPI+jncukdUPeTaIO45rtRZJ78DGn5eiDWU1B5cM1fwbxvxm+37CH0q/8PSvvk8fjH3GdYnr+YKzKbGXbR1Ty8ZUSHhLCuoZnnVjex/3gLrweHkmkTfbpCOZ53MLbHh14ygzYyCv78uqkFjhqhb6KUqtNaz06+LhF5f6MS3QRLsW8TjJkOw8bA+deZyNWOa7PC7oqim3JxW0NZvzjapDlOOwNu+j688f3AO54Q/PdPht9/1Px97VPxpw675mQXRvezXXkf7P2dcdAs/0GU4/dqUp9c3jptBpN8E4G3keVNLmEdF7BJXcStp4+nNbezw1H1s6ubwslAd8yZyLRgfFulImM3Ek5aJ2UyUP9GhHwgk8wvr1tQOjp/+X/EI9utL0WHkWAOK9ctjM/zHDLK5JmtcHsZeP95JmXSVBttAG6PcztdCOfA9MNOHjuZFqp9Ap7/pinnzw6Ovh8ecp6ClmPw+Z+ZTUU7G8pl6S0DXnl3Mq+2fYfL1WZW6YuZ+qGP87HACgh0uMAmZi30NWNHDKH5RGu3OTzam34keez+hQj5QCaW086Yw0QrrGkzON/45/jP+20UolPa3DqpDD8HB7eYf/Dgohvjh41u/v7UMRNFX3xLlKu377GbxeL7olQLmA3AiryXdQ5KnzS58+Q5QhFv+twpo/iXzEWszV3Ih7Lb+OPsIsadfx1MMCmIjgphMWHtrsi4PbGWPHb/QnLkA4m0fLg7JLnux/Hcs5siWfYQvPI/iaU8vJqg8jKInG13ws2LYPtSYhF1MbwsfPGFeBSflutetwDePQDvOysq0//xzYV5dy8LNz5krI276uCt58333c9U5rlAXUMz76x5jVvX/xGe31Yy/VSOCyTtPV11j0gV5cBCcuQDnVLTdayIum6QZN548jzInhYMVAY+/Kcw8twgpaFNRD/3j0sfaqbh+0ZU920y19K+abxl/eXvHjDOErcoac18uOyzhXl3L2MabYV9zLOmIjQ5majMc4RZk0Yya+c75smjhKWzXBdIWhTclchYqigFiwj5QKE9j3maJTHZYyX5/TDfHFS77P1dymCJdvA8k0d//puRWOdOwa/+vLgfPd8C7+4L+6SQyRpft7Ud2s/pA7O+AMPHF46kK5cwReObP1MORnurmlGqKAWLCPlAoRyPeSz3/GeBGyXIg9seK5PnGXFftwDGXBr1QvEyTvFNkZSK8gKND76vMlEaxO07rlT7laFvvYBJmXgmnePm0JO+cijPnVM05ZLWLTyit1wg4j4RLCLkA4VkxA2FjaQgSsEk0yP5NiPebim9V+PcQBnHyY0PFY+mNTDuMtPM6n1nRgeN6xaaqNq2nz17Gux/K9pEvBqTImk74VwsEHqdNykY26Dr4lvSnxzswWu+Jb3itVjqqX5ZcA4Q2CRTfra9g0WpohS6GxHygYQbcReLUG1qIhl9KmXy1bbjIcRdK37OCP3wCabsPexkGF4A8M38zuwmc09wRrt5USS+d71JY0y6Ek4cglHnQc3psP4/0z/XgS1Q+yPz9+2vGj+6e1A7ZFQU4Ws/GGCRoFjqqcxq2WK5bqmiFHoCEfJqpKuzOtNEy74+ZFQkXMqLfOLah63/FZTep9gOlYrsi1423rIWZaLw43sIBzXbe9p12OIgi5+HhjfMawfeMteLXdO573uH4q9tXmSeDtyBFXjm3nhRp0OXYoLd2aEbAZLHFnoCEfJqoxKzOpOiNWRU/JrXPwjbXjZ9UU5EzZ7wc0EuWsGedbB7TeQTP2cG7F4bHTJOnAsNvw1+UMN7+0ntHOj62LV2NonEE0Gxg08NHN4efy13ygy9sG6V6x80hUKuSKdNNyom2B2plk0geWyhJxAhrwZc0enM9J8kyeHJmxdFOfF8ixHxgtQIUQFNWnrmsj80FkL79ZkXQsNywly22/Z2zAfMe20bW9s3HYJe5+tg12pKul9GT4WDW817fN90Sjy+1/RJb3gjel++1Vw/eT5QyopZQSSPLfQEIuR9naRgJrv9uTlb98DPdXGkYQUrebCpfTi0rfD9Z4yFj/739ApMt7zeFctYj3GLNiK9q86kbjKD408VsTFyTj7ejoCzTpXRFwTVoQA+jLoAxs0yOXgXG/27Iu222+3IZtjJlJbksYXuRoS8r5OMwJPRpRWU2idgcdCOdfurJqp2S99LXTsW+XrmcPHAW/H3Ht8LL/ylaWNrLX3JNbhi2biK4hG1s2mkuUgmzDG+8NofEc6Un3oDbHs12sDedyax0v/lPzCOGc+LWxkvuK7wd9CRfuyWSqS0qhSpHu37iJD3ddJEJy0FsHlR/Ou3Fpvp9aUEx17bNqiyEfKV95kI97ffJy66rUZcV/9HdDiZjKgtoW0vgcrEDza1b3qqJK2QM+403nW3e+GV98Ujftt1EYx4nzxUaH98+yUjwqWKnyDdipn8PF1NaVUhUj1aHYiQ93XKdU1cfEvhbMxinum0aw8ZZYTQVkC2HA3SGUkx1nHXSrF7JDcJO7nnhr8PerG8RhhtL/+BSZvY1JFdR7IQJ7mBXfF1pxtjYCucfXfkKy/h/Q6/tt74Ys3Ckp+nI1F8L1HJCFpcN9WBCHk1UM4h3Oy7YdtLZpSZRXntC04yHWLTB17W5Jd9zJ8XXAdvv1yYinHvkcwhF+tiePYlUP/byOKo/SjN8vw3jagrFaRISohxyzHnC8dWOOOuwp7lSdIKn/Kt5rC1mHOlCzbEnqLSEbS4bqoDEfL+xJX3mTxyrsXkim98qGOCU6xPSbL3yponTRWmUiYqTnOxuE2v3n4p8IUvNyIORBN6FKhgLFwo3oHf2/NAq0IxtutY/ZPotUyNichtiqQ90S04H1Bm81rzZGRbTEbn3eBqqTSVjqDFdVMdiJD3dWwLV5TJG5cSks5Gje4QCLcYaM86GHxGvLfK8PGmy+HyH5goeuWjxvoXG+Rw0vQJTx525ltg6d/ByMlR2bvWMPMuUxFqR8LlW8z9r/i6mRzkNryClBYCCi64Nup6aEU4Ob7NJdmL/bLPmevZ3uZVmgfvjghaXDd9n4oIuVLqeuD7QAZ4XGv9YCWuO+BJ2vDqfgyf/MfS1sKORo3JSPryr5i2sQfeMhZBd2gxYMa0qcgKaMX54lsSOfWkYyUov9++1PRV8bIm8HaHO9QvM/df/gMTma981ET2rkBfekeK0ybItXfkMLJYt8f2UjIJ+pqjQyLogUmXhVwplQEeAT4BNAFvKqV+obXe1NVrD3jql0WNpMCI1PPfNOmJzkSKyRx24yojwm5DKXeeZSraGZXmReLcsBzeP8XxdjsoDzKnQe4E4JtofNYfmig8WaBj2wGA+XrzorhA20NTNyJXnhk40d5hZFo1Zzl58CL+8b7q6JAIeuBRiYh8DrBNa70DQCn1FHALIELeVSbPM7nfWKMqv3OP/Gk57Be/FbceqoQHuyTKDEQ+XE/YP2X0+elCrv1AxO2PKvPzNmVytCkS69gtFNQMceZ9Zk16acadUa7e5rPt68XSSuX6wJPiXuznGlfRuvTnTMufSZ2+UBwdQq9SCSEfBzQ6XzcBl1fgusKEOaYH+G+/D1teMJFwdnDnrG+xHHaLmVaft9ZAD6ZcZdIjNo0B6f1NlGf+zAw2A5HdtMeV98H518Gan5hSeesXT/YW1xrqngheDwZDpFkd/Vw0qs2mZtYtMKmYm/4pLtz2M6a15U1uFmmpl2JVm/XLos3OzgMF+PHNzM238GRNls+3fYcNmYvE0SH0GpUQcpXyWkFJn1LqXuBegIkTJ1bgtgOECXPgjvld73iY9HUffoew3D0zGK76tnnfpXcQHqy++K14jlx58Ml/MtWd7+43rhTX923X9+VXo/WeOuZ4vXFK7a24B6mWsZem5OMh5iX320xB0poFcLfTC2bfJme8W3BwOWaGWaeN2r1MkJcPrrerLioUKhWtDxkVX6v9nPlWlPY5zcvzzakHGHTV3RKNC71GJYS8CZjgfD0e2J18k9b6MeAxMMOXK3DfgUVnrW/uBnD9gyYStyJuI3Er4q6YzbjTNMJyxfXDf2r+tEOawbx37h/Da39LOG/TbULVuAqWPxIUESmY/mnY/MsoL49nRPZEc/mfKd9inlK2vRI4bBzbYj4PtT8M3uiU8PvA1Othy4tm7W/9yvji7bDo8JwgEa2fPBSldpQXNfgK8vEqM4grrvk9mCAiLvQelRDyN4ELlFLnAruAO4C7KnBdwdLZaDxZ4IOGfNBf3I3Ewyk6idSDte9tXgRjPmgKcBb/GVGEijmMfeOfnQPKRKVn/bK4k2Xjc9F4tyGjTFRf9xNo3tGx38nxPU5e3Q6lSL7JsSdmBsH7zo6nefJtwazQYBNQXuFB6eR55veUbJFQBcVBwsChy0Kutc4ppb4O/BfGfvhDrfXGLq9MMHSlWVOsP4gVsEQkbq/lpl6Uiqbo2ErMtPFvEEWr7tdJIXTfY3ui2E1i8Z8V7zUeXjNDLNfuZQvb5p7/8aCqNbG+zGC47K7I4rhmftSRMTzcdc4J3N8JFBftKigOEgYOFfGRa62fB56vxLWEBF1p1hQregkicuvySBOs6x8MSuR9k3O2Nsdi498APvwnxu9drJp0whxT2PPGP6cf1r67r/CaH/gDM5/z+B4j2GdfElRyBk2yVMa8lmx89fbLhW1z5/4RfOJvzN8bVxlRf/eA6Z445tL4YW3yd+J+BhFtoQ8jlZ19nY40a3IrNG0uNyl26xYC2kSzySjz5CEjtslccRhVJ+2Bnqm8TCusce+58tHgQSBjNgtXFN93dvya758CZ10UpF3WmdTL2ZeYilLrgvFzUerH9XqnRfZ7fxd9P+3Jxu2hXo6LRRD6ICLkfZ1y87GhUDmHiNnB8VL1xlWwdmHgXPkRpr9IxkTRs+8uvmns25RSJKRM2sKuyTpHsoOhqS7qJhhWYvqmb8rJQ3GRnHFnEGkHhU+Hd8ArD8RvtWa+OZRMW5u91q669EKmi28xfxZ7skmLttM893ZjFFEX+iAi5NVAOY/2oVA5VjlXsGwVZ9hWFsLo1q0Wvf5BWPm/TQS9L6jp+tWfU5BWmfRhuPZ75mfcoRYu+VaTxgDCTePUMfjRDSY3nckaq+CF1zl+8RTybekDNVzBTcPLRk262nuyKTpOz+nIOMAGSgjVgwh5fyEUKhuRq+jQ0o3WbW9wVzS1HxW6PP8XUXS8+BumIVayoAegcWX09+RQCyDsJrjlhSjloX1441+ir/OtxiqoMoVrcvEypqAH4o2wXMHFC4ZWOOkV7ZvNy+a+iz3ZlBqnF7M2VmcjLaH/I0LeX0j2/7aNp178Flx6ZxStq8CdMeaD0XuUFxW6uEMjwIx4S7YJgLj4504lFuOZVM27++NDnIv1cNF5jJCniblnXq/7sUkLfeEX5mX7OZUy78kMjlrnrllgPofbB8b1ticpNU4v7MhYfiMtQehpRMj7E1aolj0UVU9at4mbVrAR6shzIx/1i98yQujVxMV88jzjHFnxv+HUkShVojwjpKEt0WH23aaEfvF9HVh8UIaf9rofeN/t4Ie1C+NPHvYQ1XaFnHGXicS3L6WsSLq9cXrFDkQFoY8gQt4fSQrTjMBHXcylgm/EeO86+OLzsOR/mCgWYMX/HwyaCKJpL2t+xvejnuRu4U32NFMev+whGDy8gwu3Yp6YQKQ8c/+wqKnFSfcEa9m8KMrzT5hjDjnf+XXUKrdYJG1z46UONMV+KPRxRMiriXIscaWEKW2uppc1Ze1o05dkxp1w5tRAyHWhf9zPEYqtj/GO26jY9jixXRUVlMx9JwcxQ+LvCqbfBht/RlgQNHh4Ss7ehx1LoxTKvk3Bk0bepF5GTDTFQskBHbVPRL75tCHSYkEUqgQR8mqhnArPjlaBTphjCmTcQcV2GLEV1LCQyEbkNcEBYD4aROHO41z2UOSMCQN1J6rGeW3qDbDleae/eVL0Nax/OnrNbwvy8h7hoe37z4Xm+sj7vm5BVDgE5toHt8Tb666Zb4ZAP//N6H3J1gJdqagVhB5GhLxaKKfCM/medQvajyiTg4pRjuAqmPn5oP/3gnhFpO2VYg8C7TzOyfNMlB72NVcw9jLYu54wBz7pCvjA7eZg0ubklQcTLoeG3yYWmIjmh40xXnW73mQrXRTt9lS3Ayvc9yVbC3SlolYQehgR8mqhWC+U5Hu8jOmrolTg3si1P0ghWf25dmG8C6L9ubAB1wIzI/P43njXwHULTQXmFV+P8ueZwXDOB2H3WkyzrgyceVE0mxMFU2+EKwMf+hM3FZbZu5x/nfln86LoKeDsS6K0yZgZRuhtaifNOpkZZH62YXnx1gIdqagVhF5GhLxaKNULJUYQ9WoNui29NWvatd3vudY7azGMRahBG9jwll7hBHrb4TDcHNyoP3FgueV5OP8TRpTvXlzYB91lzU9MdO/no6eA5PXd84F9m5zujUejp4pkr5a0A85KdjiUfLvQjYiQVxPFeqFY6pdFVj2to4PIjkaUyQjcLZJJ64A45SoYOSk+gd52OGxcZSL1868xfVVm3Gl+ZvV/REKu/cLq0h/dGKRcMtF70LBrdXR/+zuwf0/e234Wa0t0895rn4q3Lyj2e6iE6Eq+XehmRMirifYe95Pf70qPkLQimesfNBHx7rVRBaU7XSg5gb5xVTxV4gX/us2400Tsv/qzuJi7G5Od6+llouEPO5Y6qZLEBlVOGiQ27u6UScd0ZvZpRyNrybcL3YwIeTXR3uO+jWZtKqErjZ6Sm4J7sOll4YLrowjb9j259E5AmwNUd1iFxc+ZUW22QvOT/xS3/4UdGheY/irWSXPykNksGpZH97c9xu1nKycNEp4hWLvlgvg12qOzkbXk24VuRoS82ij1uF/7hGlwpfOw/dVoClBnHuWTm0b9siiv7WsYNyveVTE2Ju4u89rRxmBOplv2ryOr37xvFlZN1j5hUjRu+sYe7CY3io4yYY7xutf+iFg73O6OrGWikNDNiJD3FxpXRSJuKeegsxTuprFvUzwN4rpm1i2IcuexMvpWEwGfeREceCt6v2v1c+/RuCqI0BOf4fm/iHLkXk18feBsYL7ZSO5eXMJueWfcldOR6LgrkbVUhwrdiAh5f6F+WYrVrhMHnS5uPvjkIaJCHC/qK75uAax+kqiAKEMo6HbE3KjzoLkhsk5eeH36fXatTmmspeMRfb7FCLc9rIT4BmYHM98xP/0zdSU6lsha6KOIkPcXJs+LdylUGZj1hbgP3FJuqX/SteIW4gwZlTLHU5nUxYw7g9mYQS5663+Zw03bmXDLC7DtlUiIYwMx7KUCx03qPE8dd6wk37PlBbP+5LQit1VBZ0VYImuhDyJC3l+YMAfu/lW8MObkocL3FTuwSwqemxPPtxQOdiiY4+k0zKpfBqOnwr715lt+Dra9DONmmr+7OWZIDMQIrjX1Bnh7SbAZ2Jdtz3E/3bFi0Tq6ttj+hAGACHl/wkaLpdwVaQd2UPj+IaMKc+LJaDQc7JyBC64zr73wl8ZpkoySD75tqjfTcsy2YtWdXHRoe2EPdJWBG/9X3I3TuMo8BRzYAjtXEBvwLLY/YYAgQt4fKSVgaQd2xcQ9mRN3cfPF1pqYVixkGX1B8RzzF34R9A9/Lfp593DU4ufixT7JDeuT/1houWzvcFIqLoV+gAh5f6SUu6KYmKa9382Jp4mgO8gimWbJ1ARWxZxxmtheKmlMmBP5xEttBsl1pBUtuZWa7R1OSsWl0E8QIe+PlFM45L5WKlIuJ1p1Nw63WAfizbgW31e8kZddg22jm+yDPunKaNhz2n3b22zSkNSL0E9QWheJfrqR2bNn69ra2h6/r9CNlEpR2MjXjbZVBq75bnqvk8ZV8VSL8uCav4rSQO49upIakYhcqDKUUnVa69nJ1yUirwaqIY9bTuQbS72U8LfbVEv9b4MovyayOyZFt6tWQvGFC/0AEfK+TrVEjXazGTIqGjphDx5jqZdM5DVvN6rW0Z9715ZOg3R2sxNfuNAPECHv61RDHtfOvvSDAqBwZFvQvfDGh+IOF9cBE3ZIbI2X19cvi67n5wmj+LR8eLVsdoLQTYiQ93W6u3NesUi23AjX9keJldY7kbSfM9//4gvmWknBXbcwanObbzFfT5hT+Lln3Gn+SVtTJTa7jkb01ZDuEgYMIuR9ne7M45aq8iw3wi3W48V1nPh++gCI+mUUWg2Dr4t97rR1dHWzC58ofGO5bC+ilycAoY8hQl4NdFcet1gk25EId/I80yrXrcxUCs69Gup/HYljqQEQa+ab/uOZmsi22JHP3dHNrvaJaObn2ZfEnyhyLe1H9NWQ7hIGFCLkA5likWxHIlwroq5dUPtGxN25naW86Xf/qrQIt5fG6Eiao/YJWBwUJ21/FS66Kf5E4XntR/QyKELoY4iPfKDTlRy5+x6AH14f9Vix3u9SMzHLXV+pNEZH0xz/8ftGwC3jZple6/kWs+YbH4pmfLa3LsmRCz2M+MiFdIqlL9pLa6S1uVVeJORetjKRantpjI6mOS6+JS7kl/1h4ZSichDbotCH6JKQK6X+AfgU0ApsB76otT5SgXUJfZ2kgG5eFB+MfNnnKuP+6OjA6SGjTO+XYtez0bY71xS6/uQgCL1IVyPyl4Fva61zSqn/D/g28N+7viyhz2CnAKHiRTxJAb34lmg4srULlnPt9tIi5fSNSXZhdK8HhT87+24ThYvzROgndEnItdYvOV+uAD7dteUIfYrGVfDEJ6O+4GvmRwU7aQLb0RRFuWmR9tIY9ntL/y5yz+RbzQa09qny+7KLkAtVSiVz5F8Cflrsm0qpe4F7ASZOnFjB2wrdRv0yYwu0JAUvrYtiR8SwUu6PMLK3FkjPXA/Vsb7sglCltCvkSqklwJiUb31Xa70oeM93gRxQZOItaK0fAx4D41rp1GqFniU5B7TSglepYqcwuvbNgeuUq0zTLYC1CzvWl10QqpAu2w+VUl8Avgp8XGt9opyfEfthFVEsR96XKJVrF5ug0I/oFvuhUup6zOHmx8oVcaHKcHPKSfqKSJaKrsUmKAwAupoj/wEwGHhZKQWwQmv91S6vSug7VKIfS08ggi0MYLrqWjm/UgsR+iiV6MciCEK34vX2AoQK0rjKFMM0rqrcNa27Q2XS+7EkXxcEoceREv3+QnelOkq1kxXXhyD0CUTI+wvdmerobD8WQRB6BEmt9Bck1SEIAxaJyPsLkuoQhAGLCHl/QlIdgjAgkdSKIHSH20cQehCJyIWBTV8rbBKETiARuTCwSXP7CEKVIUIuDGzE7SP0AyS1IgxsxO0j9ANEyAVB3D5ClSOpFUEQhCpHhFwQBKHKESEXBEGockTIBUEQqhwRckEQhCpHhFwQBKHKUVrrnr+pUgeAhuDL0cDBHl9Ex6mWdUL1rFXWWXmqZa2yzs4xSWt9ZvLFXhHy2AKUqtVaz+7VRZRBtawTqmetss7KUy1rlXVWFkmtCIIgVDki5IIgCFVOXxDyx3p7AWVSLeuE6lmrrLPyVMtaZZ0VpNdz5IIgCELX6AsRuSAIgtAFRMgFQRCqnD4j5EqpP1FKbVFKbVRK/X1vr6cUSqm/UEpppdTo3l5LGkqpf1BKvaWU+p1S6mdKqRG9vSYXpdT1wf/X25RS3+rt9RRDKTVBKfWaUmpz8O/lN3p7TaVQSmWUUmuUUot7ey3FUEqNUEo9E/z7uVkpdUVvr6kYSqk/C/5/36CUWqiUOq2311SMPiHkSqmrgVuAD2qtpwH/q5eXVBSl1ATgE8DO3l5LCV4GpmutPwhsBb7dy+sJUUplgEeAG4BLgDuVUpf07qqKkgO+qbW+GJgLfK0PrxXgG8Dm3l5EO3wfeFFrfREwgz66XqXUOOBPgdla6+lABrijd1dVnD4h5MAfAQ9qrVsAtNb7e3k9pfgn4L8BffaUWGv9ktY6F3y5Ahjfm+tJMAfYprXeobVuBZ7CbOJ9Dq31Hq316uDvxzGiM653V5WOUmo88Eng8d5eSzGUUmcAHwX+HUBr3aq1PtKriypNFhiilMoCQ4HdvbyeovQVIb8QmKeUWqmUel0p9aHeXlAaSqmbgV1a63W9vZYO8CXghd5ehMM4oNH5uok+Ko4uSqnJwGXAyl5eSjEexgQYfi+voxRTgAPAj4IU0ONKqdN7e1FpaK13YTIDO4E9wFGt9Uu9u6ri9NioN6XUEmBMyre+G6xjJObx9UPAfyqlpuhe8Ea2s87vANf17IrSKbVOrfWi4D3fxaQH5vfk2tpBpbzWZ59uAJRS7wOeBe7TWh/r7fUkUUrdBOzXWtcppa7q5eWUIgvMBP5Ea71SKfV94FvAX/fusgpRSo3EPCmeCxwBnlZKfU5r/WSvLqwIPSbkWutri31PKfVHwHOBcK9SSvmYZjUHemp9lmLrVEp9APN/6jqlFJh0xWql1Byt9d4eXCJQ+vcJoJT6AnAT8PHe2BBL0ARMcL4eTx9+ZFVK1WBEfL7W+rneXk8RrgRuVkrdCJwGnKGUelJr/bleXleSJqBJa22fap7BCHlf5FrgHa31AQCl1HPAh4E+KeR9JbXyc+AaAKXUhcAg+lbHMbTW67XWZ2mtJ2utJ2P+pZzZGyLeHkqp64H/DtystT7R2+tJ8CZwgVLqXKXUIMwB0i96eU2pKLNj/zuwWWv9j729nmJorb+ttR4f/Ht5B/BqHxRxgv9WGpVSU4OXPg5s6sUllWInMFcpNTT49+Dj9NGDWejBiLwdfgj8UCm1AWgFvtDHoshq4wfAYODl4Olhhdb6q727JIPWOqeU+jrwXxgnwA+11ht7eVnFuBL4PLBeKbU2eO07Wuvne29JVc+fAPODTXwH8MVeXk8qQernGWA1Jj25hj5cri8l+oIgCFVOX0mtCIIgCJ1EhFwQBKHKESEXBEGockTIBUEQqhwRckEQhCpHhFwQBKHKESEXBEGocv4PAWyK7EHGMGgAAAAASUVORK5CYII=", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "I = np.nonzero(y==0)[0]\n", "J = np.nonzero(y==1)[0]\n", "plt.plot(X[I,0], X[I,1], '.')\n", "plt.plot(X[J,0], X[J,1], '.')\n", "plt.axis('equal');" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "# on ajoute un offset aux données pour avoir un modèle affine \n", "X = np.concatenate((X,np.ones((X.shape[0],1))), axis = 1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Implémentez un gradient stochastique pour résoudre le problème de classification précédent. Affichez la fonction de coût au cours des itérations et le résultat de classification final.

" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "w0 = np.random.randn(X.shape[1],1)\n", "cout,w = exo2(X,y,w0,1e3,1)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "def l(x,w): \n", " return 1/(1+np.exp(-x.dot(w)))" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize = (15,5) )\n", "fig.add_subplot(121) \n", "plt.plot(cout)\n", " \n", "n = 100\n", "tx = np.linspace( X[:,0].min(), X[:,0].max(),num=n) \n", "ty = np.linspace( X[:,1].min(), X[:,1].max(),num=n) \n", "[B,A] = np.meshgrid( ty,tx )\n", "G = np.vstack([A.flatten(), B.flatten()]).transpose()\n", "Gwithoffset = np.concatenate((G , np.ones((G.shape[0],1))),axis=1) # on ajoute l'offset aux coordonnées\n", " \n", "fig.add_subplot(122)\n", "plt.imshow(l(Gwithoffset,w).reshape((n,n)), origin=\"lower\", extent=[tx.min()-2,tx.max()+2,ty.min(),ty.max()],cmap ='viridis' )\n", "plt.axis('equal')\n", "plt.plot(X[I,0], X[I,1], '.')\n", "plt.plot(X[J,0], X[J,1], '.')\n", "plt.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**SGA**

\n", "Faites la même expérience avec un gradient stochastique moyenné (SGA). L'idée est de calculer le nouveau vecteur wnew puis de mettre à jour w en posant : \n", " \n", "$$ w = \\frac w {k+1}+w_{new}* \\frac {k} {k+1}$$

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Classification binaire sur les (0,1) de MNIST\n", "\n", "On va maintenant appliquer le même principe que précédemment pour de la classification binaire en grande dimension. On utilise pour cela une base d'images de chiffres manuscrits appelée MNIST. On a extrait de cette base seulement les 0 et les 1. " ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(12665, 785)" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "mnist = np.array(pd.read_csv('../data/mnist_train01.csv'))\n", "mnist = mnist[:,1:] # on enlève la première colonne qui correspond aux labels\n", "mnist.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Le tableau `mnist` contient 12665 lignes et 785 colonnes. Chaque ligne correspond à un vecteur de données de taille 784 (une image 28 x 28). La première colonne correspond à la classe du vecteur. On affiche quelques-unes de ces images." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "X = mnist[:,1:]\n", "y = mnist[:,0].reshape(X.shape[0],1)\n", "\n", "k = np.random.randint(0,mnist.shape[0],20)\n", "\n", "for i in range(20):\n", " plt.subplot(4,5,i+1)\n", " plt.imshow(X[k[i],:].reshape(28,28), cmap=\"gray\")\n", " plt.axis('off')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pour limiter le temps de calcul on va réduire la taille de ces images d'un facteur 2 dans chaque dimension pour obtenir des images de taille 14 x 14 soit des données dans un espace de dimension 196." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "X = X.reshape(X.shape[0],28,28)\n", "X = X[:,::2,::2]\n", "X = X.reshape(X.shape[0],X.shape[1]*X.shape[2])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On normalise l'ensemble des données et on ajoute un offset." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "mu = np.mean(X,0)\n", "sigma = np.std(X,0)\n", "X = X-mu # on centre les données\n", "X = X/(sigma+1e-5) # on normalise les données\n", "\n", "X = np.concatenate((X,np.ones((X.shape[0],1))), axis = 1) # on ajoute un offset aux données pour avoir un modèle affine" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Utilisez maintenant la même approche que précédemment pour classer nos données en grande dimension. Observez si votre algorithme converge en fonction de votre initialisation de w.

" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "w0 = 0.01*np.random.randn(X.shape[1],1) # initialisation aléatoire\n", "cout,w = exo2(X,y,w0,1e4,0.1) # descente de gradient stochastique" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(cout)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On peut calculer le taux de réussite sur la base d'apprentissage." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.9967627319384129" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.mean((1/(1+np.exp(-X.dot(w)))>0.5)*1==y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Calculez maintenant le taux de réussite sur la base de test `mnist_test01.csv`. Quel taux obtenez-vous ? N'oubliez pas de centrer et normaliser les données de test

" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.9985815602836879" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#lecture des données de test\n", "mnist_test = np.array(pd.read_csv('../data/mnist_test01.csv'))\n", "mnist_test = mnist_test[:,1:]\n", "X_test = mnist_test[:,1:]\n", "y_test = mnist_test[:,0].reshape(X_test.shape[0],1)\n", "# sous-échantillonnage (on ne garde que la moitié des pixels dans chaque dimension, on retransforme donc les données en images)\n", "X_test = X_test.reshape(X_test.shape[0],28,28)\n", "X_test = X_test[:,::2,::2]\n", "X_test = X_test.reshape(X_test.shape[0],X_test.shape[1]*X_test.shape[2])\n", "# centrage et normalisation\n", "X_test = X_test-np.mean(X_test,0)\n", "X_test = X_test/(np.std(X_test,0)+1e-5)\n", "# ajout de l'offset\n", "X_test = np.concatenate((X_test,np.ones((X_test.shape[0],1))), axis = 1)\n", "# calcul de la précision\n", "np.mean((1/(1+np.exp(-X_test.dot(w)))>0.5)*1==y_test)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "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": "3.10.4" } }, "nbformat": 4, "nbformat_minor": 2 }