{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Entropic Regularization of Optimal Transport\n", "============================================\n", "\n", "*Important:* Please read the [installation page](http://gpeyre.github.io/numerical-tours/installation_matlab/) 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 numerical tours exposes the general methodology of regularizing the\n", "optimal transport (OT) linear program using entropy. This allows to\n", "derive fast computation algorithm based on iterative projections\n", "according to a Kulback-Leiber divergence.\n", "$$\\DeclareMathOperator{\\KL}{KL}\n", "\\newcommand{\\KLdiv}[2]{\\KL\\pa{#1 | #2}}\n", "\\newcommand{\\KLproj}{\\text{Proj}^{\\tiny\\KL}}\n", "\\renewcommand{\\epsilon}{\\varepsilon}\n", "\\def\\ones{\\mathbb{I}}$$" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from __future__ import division\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy as scp\n", "import pylab as pyl\n", "\n", "import warnings\n", "warnings.filterwarnings('ignore')\n", "\n", "%matplotlib inline\n", "%load_ext autoreload\n", "%autoreload 2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Entropic Regularization of Optimal Transport\n", "--------------------------------------------\n", "We consider two input histograms $a,b \\in \\Si_n$, where we denote the simplex in $\\RR^n$\n", "$$\\Si_n \\eqdef \\enscond{ a \\in \\RR_+^n }{ \\sum_i a_i = 1 }.$$\n", "We consider the following discrete regularized transport\n", "$$W_\\epsilon(a,b) \\eqdef \\umin{P \\in U(a,b)} \\dotp{C}{P} - \\epsilon E(P).$$\n", "where the polytope of coupling is defined as\n", "$$U(a,b) \\eqdef \\enscond{P \\in (\\RR^+)^{n \\times m}}{ P \\ones_m = a, P^\\top \\ones_n = b },$$\n", "where $\\ones_n \\eqdef (1,\\ldots,1)^\\top \\in \\RR^n$,\n", "and for $P \\in \\RR_+^{n \\times m}$, we define its entropy as\n", "$$E(P) \\eqdef -\\sum_{i,j} P_{i,j} ( \\log(P_{i,j}) - 1).$$\n", "\n", "\n", "When $\\epsilon=0$ one recovers the classical (discrete) optimal transport.\n", "We refer to the monograph [Villani](#biblio) for more details about OT.\n", "The idea of regularizing transport to allows for faster computation is\n", "introduced in [Cuturi](#biblio).\n", "\n", "\n", "Here the matrix $C \\in (\\RR^+)^{n \\times m}$ defines the ground cost, i.e.\n", "$C_{i,j}$ is the cost of moving mass from a bin indexed by $i$ to a bin indexed by $j$.\n", "\n", "\n", "The regularized transportation problem can be re-written as a projection\n", "$$W_\\epsilon(a,b) = \\epsilon \\umin{P \\in U(a,b)} \\KLdiv{P}{K}\n", "\t\\qwhereq\n", "\tK_{i,j} \\eqdef e^{ -\\frac{C_{i,j}}{\\epsilon} }$$\n", "of the Gibbs kernel $K$ according to the Kullback-Leibler divergence.\n", "The Kullback-Leibler divergence between $P, K \\in \\RR_+^{n \\times m}$ is\n", "$$\\KLdiv{P}{K} \\eqdef \\sum_{i,j} P_{i,j} \\pa{ \\log\\pa{ \\frac{P_{i,j}}{K_{i,j}} } - 1}.$$\n", "\n", "\n", "This interpretation of regularized transport as a KL projection and its numerical\n", "applications are detailed in [BenamouEtAl](#biblio).\n", "\n", "\n", "Given a convex set $\\Cc \\subset \\RR^N$, the projection according to the Kullback-Leiber divergence is defined as\n", "$$\\KLproj_\\Cc(\\xi) = \\uargmin{ \\pi \\in \\Cc } \\KLdiv{\\pi}{\\xi}.$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Iterative Bregman Projection Algorithm\n", "--------------------------------------\n", "Given affine constraint sets $(\\Cc_1,\\Cc_2)$, we aim at computing\n", "$$\\KLproj_\\Cc(K) \\qwhereq \\Cc = \\Cc_1 \\cap \\Cc_2$$\n", "(this description can of course be extended to more than 2 sets). \n", "\n", "This can be achieved, starting by $P_0=K$, by iterating $\\forall \\ell \\geq 0$, \n", "$$P_{2\\ell+1} = \\KLproj_{\\Cc_1}(P_{2\\ell}) \n", " \\qandq \n", " P_{2\\ell+2} = \\KLproj_{\\Cc_2}(P_{2\\ell+1}).$$\n", "\n", "One can indeed show that $P_\\ell \\rightarrow \\KLproj_\\Cc(K)$.\n", "We refer to [BauschkeLewis](#biblio) for more details about this\n", "algorithm and its extension to compute the projection on the intersection of\n", "convex sets (Dikstra algorithm)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Sinkhorn's Algorithm\n", "-----------------------------------------------------------------------\n", "\n", "A fundamental remark is that the optimality condition of the entropic regularized problem shows that the optimal coupling $P_\\epsilon$ necessarily has the form \n", "$$P_\\epsilon = \\diag{u} K \\diag{v}$$\n", "where the Gibbs kernel is defined as\n", "$$K \\eqdef e^{-\\frac{C}{\\epsilon}}.$$\n", "\n", "One thus needs to find two positive scaling vectors $u \\in \\RR_+^n$ and $v \\in \\RR_+^m$ such that the two following equality holds\n", "$$P \\ones = u \\odot (K v) = a \n", "\\qandq\n", "P^\\top \\ones = v \\odot (K^\\top u) = b.$$\n", "\n", "Sinkhorn's algorithm alternate between the resolution of these two equations, and reads\n", "$$u \\longleftarrow \\frac{a}{K v} \\qandq v \\longleftarrow \\frac{b}{K^\\top u}.$$\n", "This algorithm was shown to converge to a solution of the entropic regularized problem by [Sinkhorn](#biblio)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Transport Between Point Clouds\n", "------------------------------\n", "We first test the method for two input measures that are uniform measures\n", "(i.e. constant histograms) supported on two point clouds\n", "(that do not necessarily have the same size).\n", "\n", "\n", "We thus first load two points clouds $x=(x_i)_{i=1}^{n}, y=(y_i)_{i=1}^{m},$\n", "where $x_i, y_i \\in \\RR^2$.\n", "\n", "\n", "Number of points in each cloud, $N=(n,m)$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "N = [300,200]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Dimension of the clouds." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "d = 2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Point cloud $x$, of $n$ points inside a square." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "x = np.random.rand(2,N[0])-.5" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Point cloud $y$, of $m$ points inside an anulus." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "theta = 2*np.pi*np.random.rand(1,N[1])\n", "r = .8 + .2*np.random.rand(1,N[1])\n", "y = np.vstack((np.cos(theta)*r,np.sin(theta)*r))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Shortcut for displaying point clouds." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "plotp = lambda x,col: plt.scatter(x[0,:], x[1,:], s=200, edgecolors=\"k\", c=col, linewidths=2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Display of the two clouds." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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CG7QB+AxQxvT6CuC/YJSw+zCKXGBWFqXIaAGqlM0hAvnBUmjKDUckSXImcA3w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FaWNP6mPWURY6mQ0Zgnp5ii7zCIKQpXIhi1sv25Of4N4lb8PJURQthSZYIGeK0Y+t/Ew9ImcH3F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\n940fchSjHxzoWCGDSNfspzCKZ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,10))\n", "\n", "plotp(x, 'b')\n", "plotp(y, 'r')\n", "\n", "plt.axis(\"off\")\n", "plt.xlim(np.min(y[0,:])-.1,np.max(y[0,:])+.1)\n", "plt.ylim(np.min(y[1,:])-.1,np.max(y[1,:])+.1)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Cost matrix $C_{i,j} = \\norm{x_i-y_j}^2$." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "x2 = np.sum(x**2,0)\n", "y2 = np.sum(y**2,0)\n", "C = np.tile(y2,(N[0],1)) + np.tile(x2[:,np.newaxis],(1,N[1])) - 2*np.dot(np.transpose(x),y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Target histograms $(a,b)$, here uniform histograms." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "a = np.ones(N[0])/N[0]\n", "b = np.ones(N[1])/N[1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Regularization strength $\\epsilon>0$." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "epsilon = .01;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Gibbs Kernel $K$." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "K = np.exp(-C/epsilon)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Initialization of $v=\\ones_{m}$ ($u$ does not need to be\n", "initialized)." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "v = np.ones(N[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One sinkhorn iterations." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "u = a / (np.dot(K,v))\n", "v = b / (np.dot(np.transpose(K),u))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Exercise 1__\n", "\n", "Implement Sinkhorn algorithm.\n", "Display the evolution of the constraints satisfaction errors\n", "$$\\norm{ P \\ones - a }_1 \\qandq \\norm{ P^\\top \\ones - b }$$\n", "(you need to think about how to compute these residuals from $(u,v)$ alone).\n", "isplay the violation of constraint error in log-plot." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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apiSQkRpPy5TAV6uUBFqmxNMiOY5YLWkhIihwiUiUiY3x0S0jhW4ZKT845vc7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\ngg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "run -i nt_solutions/optimaltransp_5_entropic/exo1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compute the final matrix $P$." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "P = np.dot(np.dot(np.diag(u),K),np.diag(v))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Display it." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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l4Orppq9EtWVLEI2O5nLbUcjbK5qiMZTdjCIvyJqqbSEwNmHmPxEqknYe3/7O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\nQVRKGIxbsLR7pQEuX3+2XlIo+iEbqqP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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(P);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Exercise 2__\n", "\n", "Display the regularized transport solution for various values of $\\epsilon$.\n", "For a too small value of $\\epsilon$, what do you observe ?" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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rQPsHQSUZNBJG4Ko2VSIXYPHwnC4Zk/WstDBnt4MrKWI3NBb62Fx0wpy9ph32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4F7IDoALz8jhnWN8N3cGYvDzrY2ISRc+a3fRWA5SYrxtkmRP6NQkOB45dqbvtvO9aGrPvwY8X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\nTUtW/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7UW95ZLi+dzu3HYgSI1fpSn84kSMbs/MxPaqFpmR7una9OV9aZ4X98HIooxJiS0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\nCFjGJKgFGccIIaqb+sJUjCqMYeMBpBeZrEYt3He1ICOgv5wnA7hFC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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "run -i nt_solutions/optimaltransp_5_entropic/exo2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compute the obtained optimal $P$." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "P = np.dot(np.dot(np.diag(u),K),np.diag(v))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Keep only the highest entries of the coupling matrix, and use them to\n", "draw a map between the two clouds.\n", "First we draw \"strong\" connexions, i.e. linkds $(i,j)$ corresponding to\n", "large values of $P_{i,j}$.\n", "We then draw weaker connexions." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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LZXKkFE+BP2MOVFlQ3kbpHdveJ2hzMopLtkWzx1/m2JIQFqNsOVc1u71Jn0J12OrgP8xc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N4DRbpNRBaIJsAxiKN3v9fzaBQJNxBZU2dH94tKAEHfWyqK1eAYk4bZDVYs1psupZYcxOuJIzBv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2J2Jk+mORciM4g+yBNp4PoV1DFUKC7xJz6Hbx8dOlPv3fMM+sLmOq7PGN4kBAYWaSNsgprKvX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\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vEKuRbkUgMGmI8D6S/OyL8c1y3rMs2jx0suMlgK1y7l+MGHzeQ+xKwkvKXsvIN4icKAaJ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,10))\n", "\n", "plotp(x, 'b')\n", "plotp(y, 'r')\n", "\n", "A = P * (P > np.max(P)*.8)\n", "i,j = np.where(A != 0)\n", "plt.plot([x[0,i],y[0,j]],[x[1,i],y[1,j]],'k',lw = 2)\n", "\n", "A = P * (P > np.max(P)*.2)\n", "i,j = np.where(A != 0)\n", "plt.plot([x[0,i],y[0,j]],[x[1,i],y[1,j]],'k:',lw = 1)\n", "\n", "plt.axis(\"off\")\n", "plt.xlim(np.min(y[0,:])-.1,np.max(y[0,:])+.1)\n", "plt.ylim(np.min(y[1,:])-.1,np.max(y[1,:])+.1)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Transport Between Histograms\n", "----------------------------\n", "We now consider a different setup, where the histogram values\n", "$a,b$ are not uniform, but the measures are defined on a uniform grid\n", "$x_i=y_i=i/n$. They are thue often refered to as \"histograms\".\n", "\n", "\n", "Size $n$ of the histograms." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "N = 200" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We use here a 1-D square Euclidean metric." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "t = np.arange(0,N)/N" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define the histogram $a,b$ as translated Gaussians." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "Gaussian = lambda t0,sigma: np.exp(-(t-t0)**2/(2*sigma**2))\n", "normalize = lambda p: p/np.sum(p)\n", "\n", "sigma = .06;\n", "a = Gaussian(.25,sigma)\n", "b = Gaussian(.8,sigma)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Add some minimal mass and normalize." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "vmin = .02;\n", "a = normalize( a+np.max(a)*vmin)\n", "b = normalize( b+np.max(b)*vmin)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Display the histograms." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize = (10,7))\n", "\n", "plt.subplot(2, 1, 1)\n", "plt.bar(t, a, width = 1/len(t), color = \"darkblue\")\n", "plt.subplot(2, 1, 2)\n", "plt.bar(t, b, width = 1/len(t), color = \"darkblue\")\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Regularization strength $\\ga$." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "epsilon = (.03)**2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Gibbs kernel is a Gaussian convolution,\n", "$$K_{i,j} \\eqdef e^{ -(i/N-j/N)^2/\\epsilon }.$$" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "[Y,X] = np.meshgrid(t,t)\n", "K = np.exp(-(X-Y)**2/epsilon)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Initialization of $v=\\ones_{N}$." ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "v = np.ones(N)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One sinkhorn iteration." ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "u = a / (np.dot(K,v))\n", "v = b / (np.dot(np.transpose(K),u))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Exercise 3__\n", "\n", "Implement Sinkhorn algorithm.\n", "Display the evolution of the constraints satisfaction errors\n", "$\\norm{ P \\ones - a }_1, \\norm{ P^\\top \\ones - b }_1$. You need to think how to compute it from $(u,v)$.\n", "Display the violation of constraint error in log-plot." ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "image/png": 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SEZGk1z8U4O9fPMH3Xzn1nvGKgiy2rHJS5XIwqyiXlBQtIyHXTmFLRERkjFOt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\nMoKUbImIiIiMICVbIiIiIiPo/wHKBUxRAFgMwQAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "run -i nt_solutions/optimaltransp_5_entropic/exo3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Display the coupling. Use a log domain plot to better vizualize it." ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "image/png": 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iqnH8MQYc5oBDPSdwPHY4HMobOd45hA+K7n352v6tw/C2x+6Xm/Lav76EvvsIu70tv9Px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\nzdDJrUezba3IAnUpwKDIQ5E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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P = np.dot(np.dot(np.diag(u),K),np.diag(v))\n", "plt.figure(figsize=(5,5))\n", "plt.imshow(np.log(P+1e-5))\n", "plt.axis('off');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One can compute an approximation of the transport plan\n", "between the two measure by computing the so-called barycentric projection map\n", "$$t_i \\in [0,1] \\longmapsto s_j \\eqdef \\frac{\\sum_{j} P_{i,j} t_j }{ \\sum_{j} P_{i,j} }\n", " = \\frac{ [u \\odot K(v \\odot t)]_j }{ a_i }.$$\n", "where $\\odot$ and $\\frac{\\cdot}{\\cdot}$ are the enry-wise multiplication and division.\n", "\n", "\n", "This computation can thus be done using only multiplication with the\n", "kernel $K$." ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [], "source": [ "s = np.dot(K,v*t)*u/a" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Display the transport map, super-imposed over the coupling." ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "image/png": 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88AD/wZf+O9llJGYnCFcDkaL3i4sUX92oXgp+dp3aL7zwOhj7DbHsBGG3KK0h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\n/1FOAUU0yHhgAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(5,5))\n", "plt.imshow(np.log(P+1e-5))\n", "plt.plot(s*N,t*N, 'r', linewidth=3);\n", "plt.axis('off');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Exercise (bonus)__\n", "\n", "Try different regularization strength $\\epsilon$." ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "9RPBqH0Ezjvh" }, "source": [ "Using GPUs\n", "-----------------------" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "kGhILmt9xu8B" }, "source": [ "We will use here [Pytorch](https://pytorch.org/) to implement Sinkhorn on the GPU. If you are running the code on Google Colab, this means you need to switch on in the preferences the use of a GPU." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 34 }, "colab_type": "code", "id": "NAHof2CXyV4L", "outputId": "a652c997-1ad1-46e5-a35f-85e7a067be88" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "cpu\n" ] } ], "source": [ "import torch\n", "device = torch.device(\"cuda:0\" if torch.cuda.is_available() else \"cpu\")\n", "print( device )" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "D9BNJqSN_5V1" }, "source": [ "Since CUDA uses float number on 32 bits, one needs to use a quite large value for $\\epsilon$ to avoid overflow." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "colab": {}, "colab_type": "code", "id": "deGYKr51_3wg" }, "outputs": [], "source": [ "epsilon = (.06)**2\n", "K = np.exp(-(X-Y)**2/epsilon)" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "43VLmQHb0_4J" }, "source": [ "Convert Sinkohrn variables and host them on GPU (if available)." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "colab": {}, "colab_type": "code", "id": "vNoqBwVQ0O2D" }, "outputs": [], "source": [ "u = torch.ones(N);\n", "v = torch.ones(N);\n", "K1 = torch.from_numpy(K).type(torch.FloatTensor); \n", "a1 = torch.from_numpy(a).type(torch.FloatTensor); \n", "b1 = torch.from_numpy(b).type(torch.FloatTensor); \n", "# send them to the GPU\n", "K1 = K1.to(device);\n", "u = u.to(device); \n", "v = v.to(device);\n", "a1 = a1.to(device); \n", "b1 = b1.to(device);" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "hbBZMACcATWx" }, "source": [ "When using Pytorch, it is good practice to implement matrix operation as summation and dummy variables. We show here how to implement one iteration of Sinkhorn this way." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "colab": {}, "colab_type": "code", "id": "JC99FbLs1WDF" }, "outputs": [], "source": [ "u = a1 / (K1 * v[None,:]).sum(1)\n", "v = b1 / (K1 * u[:,None]).sum(0)" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "x8vB89l4AyQL" }, "source": [ "__Exercise:__\n", "\n", "Implement the full algorithm." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 446 }, "colab_type": "code", "id": "MeUfBp5z0FBd", "outputId": "489a0bd7-c773-42c5-f5e9-25d2f1aa61c8" }, "outputs": [ { "data": { "image/png": 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\n", 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