{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Phase transition diagrams of the Basis Pursuit algorithm for various random matrices with different \"concentration properties\"\n", "===================================\n", "\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", "$\\newcommand{\\R}{\\mathbb{R}}$\n", "$\\newcommand{\\E}{\\mathbb{E}}$\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", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook provides empirical evidences to the theoretical results from \n", "\n", ">\"On the gap between RIP-properties and sparse recovery conditions\" Sjoerd Dirksen, Guillaume Lecué, Holger Rauhut\n", "\n", "available at http://arxiv.org/abs/1504.05073" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "from __future__ import division\n", "import numpy as np\n", "%pylab inline\n", "#%load_ext autoreload\n", "#%autoreload 2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compressed Sensing Recovery with the Douglas-Rachford algorithm\n", "------------------------------------\n", "In Compressed sensing, one is given a highly underdetermined linear system with $m$ equations and $n$ unknown variables with $n>>m$: find $\\hat x$ such that $y=A \\hat x$ where $A\\in\\R^{m\\times n}$ is a compression matrix, i.e. $n>m$. This problem is ill posed because $\\hat x$ is higher dimensional than $y$ and so there is an infinite number of solutions. What saves the day is that the target vector $\\hat x$ we want to recover is sparse in the sense that it has a short support.\n", "\n", "A natural idea is therefore to look for the vector with the shortest support in the space of solutions but this problem is usually NP-hard because the function \"size of the support\" of a vector is not convex. So one may look for the convex function the \"closest\" to the last one, which is here the $\\ell_1$-norm. So we end up with a procedure that aims to find the solution with the smallest $\\ell_1$ norm:\n", "$$x_{recovered} \\in \\arg\\min_{x\\in\\R^n} \\norm{x}_1 \\quad\\mbox{s.t.}\\quad Ax=y$$\n", "where the $\\ell^1$ norm is defined as\n", "$$\\norm{x}_1 = \\sum_{j=1}^n \\abs{x_j}.$$\n", "This procedure is called the **basis pursuit**.\n", "\n", "\n", "It is a convex optimization problem of a non-smooth function under affine\n", "constraints. This can be shown to be equivalent to a linear programming\n", "problem, for which various algorithms can be used (simplex, interior\n", "points). We propose here to use the Douglas-Rachford algorithm." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Douglas-Rachford Algorithm\n", "--------------------------\n", "The Douglas-Rachford (DR) algorithm is an iterative scheme designed to solve convex optimization of the form\n", "$$\\umin{x} f(x) + g(x)$$\n", "where $f$ and $g$ are convex functions, of which one is able to\n", "compute the proximal operators.\n", "\n", "We recall that the proximal operator of a function $h$ is defined by\n", "$$\\mathrm{prox}_{h}(x) \\in {\\rm argmin}_{u\\in\\R^N}\\Big(\\frac{1}{2}\\norm{x-u}_2^2+h(u)\\Big)$$\n", "\n", "The Douglas-Rachford algorithm takes an arbitrary initialization element $s^{(0)}$, a parameter $\\ga>0$ and iterates, for $k=1,2,\\ldots$\n", "\n", "$$\n", "\\left|\\begin{array}{l}\n", "x^{(k)} = \\mathrm{prox}_{\\gamma f} (s^{(k-1)} )\\\\\n", "z^{(k)} = \\text{prox}_{\\ga g}( 2x^{(k)}-s^{(k-1)})\\\\\n", "s^{(k)} = s^{(k-1)}+ z^{(k)}-x^{(k)}.\n", "\\end{array}\\right.\n", "$$\n", "\n", "It is of course possible to inter-change the roles of $f$ and $g$,\n", "which defines a different algorithm.\n", "\n", "The iterates $x^{(k)}$ converge to a solution of the minimization problem $\\min f+g$. DR algorithm can be understood as an approximation of a fixed point solution to\n", "$$\n", "s = F(s) \\mbox{ where } F(s) = s + \\mathrm{prox}_{\\gamma f}(2\\mathrm{prox}_{\\gamma g}(s)- s) - \\mathrm{prox}_{\\gamma g}(s)\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Implementation of the Basis Pursuit via the Douglas-Rachford algorithm\n", "---------------------------------\n", "It is possible to recast the basis pursuit procedure as the minimization of a sum $f+g$\n", "where $g(x) = \\norm{x}_1$ and $f(x)=\\iota_{\\Omega}$ where $\\Omega =\n", "\\enscond{x}{Ax=y}$ is an affine space, and $\\iota_\\Omega$ is the indicator\n", "function\n", "$$\\iota_\\Omega(x) = \\choice{ 0 \\qifq x \\in \\Omega, \\\\ +\\infty \\qifq x \\notin \\Omega. }$$\n", "\n", "\n", "The proximal operator of the $\\ell^1$ norm is a soft thresholding operator:\n", "$$\\text{prox}_{\\gamma \\norm{\\cdot}_1}(x)_j = \\max\\pa{ 0, 1-\\frac{\\ga}{\\abs{x_j}} } x_j, \\quad j=1,\\ldots,n$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Phase transition diagrams\n", "A phase transition diagram is a usefull (simulation) tool to answer the following question:\n", "\n", "> Given a compression matrix $A$ of size $m\\times n$ and a reconstrcution algorithm (for instance the Basis Pursuit via Douglas-Rachford) what is the maximal sparsity parameter $s$ such that \"many\" $s$-sparse signal $\\hat x\\in\\R^n$ can be exactly reconstructed from $y=A\\hat x$ (and $A$) using the algorithm?\n", "\n", "To answer this question, we iterate over $s=1,2,\\cdots,m$ (no need to go beyond $m$) and for each $s$ we simulate *nbtest* signals $\\hat x$ with sparsity $s$, run the reconstruction algorithm with $y=A\\hat x$ and check if the reconstruction is exact (that is, let say, $||x_{restored} - \\hat x||_2\\leq 0.001$). If the reconstruction is exact for the *nbtest* signals then we plot a white pixel if reconstruction failed for all *nbtest* signals then we plot a black pixel. For every result inbetween we plot a grey pixel. (in what follows, we use colour red in place of the white colour and colour blue in place of black colour).\n", "\n", "This gives a line of the diagram matrix for a given number of measurements $m$. Then, we repeat this construction for all $m=1,2,\\ldots,n$. \n", "\n", "We end up with a $n\\times n$ matrix and use some heatmap representation to draw the phase transition diagram. (Actually, we stop at $s\\leq n/2$ since the proportional case $s\\sim m \\sim n$ is not very interesting in Compressed sensing (even though this regime, sometimes called the \"Kashin regime\", has been extensively studied in the theory of Banach spaces since Dvoretsky theorem)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Douglas-Rachford procedure" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#proximal operator of \\ell_1 norm\n", "def prox_gamma_g(x, gamma):\n", " return x - x/maximum(abs(x)/gamma,1) # soft-thresholding\n", "\n", "#proximal operator of the indicator function of an affine space \n", "def prox_f(x, y, A, pA):\n", " return x + pA.dot(y-A.dot(x))\n", "\n", "def DR(n, y, A, pA, nbiter, gamma):\n", " s = zeros(n)\n", " for iter in range(nbiter): # iter goes from 0 to nbiter-1\n", " x = prox_f(s, y, A, pA)\n", " z = prox_gamma_g(2*x-s, gamma)\n", " s = s + z - x\n", " return x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Phase transition matrix" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#initialization of the seed for reproducibility\n", "random.seed(0)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def signal(n, sparsity):\n", " sel = random.permutation(n)\n", " sel = sel[0:sparsity] # indices of the nonzero elements of xsharp\n", " xsharp = zeros(n)\n", " xsharp[sel] = 1\n", " return xsharp" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def phase_transition_mat(n, nbiter, gamma, nbtest):\n", " \"\"\"return a n.n matrix with the number of reconstruction success for every 1\\leq m \\leq n measurements \n", " and sparsity 1\\leq s\\leq n/2\n", " n : ambiant dimension of the signals\n", " nbiter : number of iteration in the DR algorithm\n", " gamma : threshold parameter in the soft threshold proximal function\n", " nbtest : number of tests for each pixel\"\"\"\n", " PTM = zeros((n,int(n/2)))\n", " set_ind_failure = []\n", " for m in range(1,n+1):#construct one line of the Phase transition matrix for a given number of measurements P\n", " if (m % 20) == 0:\n", " print(\"line number {} done\".format(m))\n", " A = randn(m,n) / sqrt(m)\n", " pA = pinv(A) # pseudo-inverse. Equivalent to pA = A.T.dot(inv(A.dot(A.T)))\n", " ind_failure = 0\n", " for sparsity in range(1,min(m, int(n/2))+1):\n", " nb_success = 0 \n", " for i in range(nbtest):\n", " xsharp = signal(n, sparsity)\n", " y = A.dot(xsharp)\n", " x_restored = DR(n, y, A, pA, nbiter, gamma)\n", " if norm(x_restored-xsharp, ord=2) <0.001:\n", " nb_success = nb_success + 1\n", " PTM[m-1, sparsity-1] = nb_success\n", " return PTM" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Construction of the Phase transition matrix\n", "\n", "> n: the size of the ambiant space\n", "\n", "> nbiter: the number of iteration in the Douglas Rachford algorithm\n", "\n", "> gamma: theshold parameter in the soft thresholding operator\n", "\n", "> nbtest: number of test (=number of signals) constructed for each pixel" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "line number 20 done\n" ] } ], "source": [ "n, nbiter, gamma, nbtest = 30, 20, 1, 10\n", "mat = phase_transition_mat(n, nbiter, gamma, nbtest)# construction of the matrix with the number of success among nbtest" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Construction of the 'frontier'" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def frontier(mat, n):\n", " \"\"\"construction of the phase transition frontier, i.e. first time the number of success goes below nbtest/2\"\"\"\n", " L = []\n", " N = len(mat)\n", " for s in range(int(n/2)):\n", " m = 0\n", " while mat[m,s]" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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CVZCDNwLIpiA6AnDWXZIGZI45KOjKFuiWoDPQmRgJOEIrhNbMFupoiLnlnfO8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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P_min, P_max, S_min, S_max = 0, n, 0, int(n/2)\n", "fig = plt.imshow(mat[P_min:P_max, S_min:S_max], interpolation=\"gaussian\", \n", " aspect='auto', origin = 'lower', extent=[S_min, S_max, P_min, P_max])\n", "titre = \"Gaussian measurements\"\n", "plt.title(titre)\n", "plt.xlabel('sparsity')\n", "plt.ylabel('number of measurements')\n", "\n", "#empirical phase transition\n", "X = range(int(n/2))\n", "L = frontier(mat, n)\n", "plot(X,L, linewidth=4, color = 'black', label='phase transition')\n", "plt.legend(loc=4)\n", "#Theoretical phase transition curve\n", "#Y = [3*s*log(0.6*N/(s+1)) for s in X]\n", "#plot(X,Y, linewidth=3, color = 'white')\n", "\n", "#plt.savefig(\"gaussian_100.png\",bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "### repeat the construction of the frontier a hundred times to \"smooth it\"\n", "\n", "> nb_curves: number of phase transition curves constructed. Those curves are then averaged in order to \"smooth\" the effect of randomness and get a \"stable\" phase transition" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "step 0 done\n", "line number 20 done\n", "line number 20 done\n", "line number 20 done\n", "line number 20 done\n", "line number 20 done\n", "line number 20 done\n", "line number 20 done\n", "line number 20 done\n", "line number 20 done\n", "line number 20 done\n" ] } ], "source": [ "n, nbiter, gamma, nbtest, nb_curves = 30, 20, 1, 10, 10\n", "L = zeros(int(n/2))\n", "for i in range(nb_curves):\n", " if (i % 10) == 0:\n", " print('step {} done'.format(i))\n", " mat = phase_transition_mat(n, nbiter, gamma, nbtest)\n", " F = frontier(mat, n)\n", " L = [sum(a) for a in zip(L,F)] \n", "L_gauss = [i/nb_curves for i in L]" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#For next use, save the Gaussian phase transition frontier in the 'gaussian_phase_transition_n.p' file\n", "import pickle\n", "filename = 'gaussian_phase_transition_n_{}_nbtest_{}_nbcurves_{}.p'.format(n, nbtest, nb_curves)\n", "#for saving\n", "#with open(filename, \"wb\") as f:\n", "# pickle.dump(L_gauss, f)\n", "#for loading\n", "with open(filename, \"rb\") as f:\n", " L_gauss = pickle.load(f)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Draw the phase transition frontier for Gaussian measurements" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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N4rAkYEyElLRL52WXwQkn+B6eSVCWBIzxUUm6dF56KVx+uXXpNJFhScCYMmZdOk08sSRg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\nhPu9v/XWW9q1a9eg2K688kp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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = range(len(L_gauss))\n", "plot(X,L_gauss, linewidth=4, color = 'blue', label=\"Gaussian phase transition\")\n", "titre = \"Gaussian measurements\"\n", "plt.title(titre)\n", "plt.xlabel('sparsity')\n", "plt.ylabel('number of measurements')\n", "plt.legend(loc=4)\n", "#plt.savefig(\"phase_transition_curve_gaussian_100.png\",bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Construction of (smoothed) phase transition frontiers for other type of measurements\n", "\n", "In the two papers (available [here](http://lecueguillaume.github.io/research/))\n", "> S. Dirksen, G. Lecué and H. Rauhut.\n", "*On the gap between RIP-properties and sparse recovery conditions*\n", "\n", ">G. Lecué and S. Mendelson.\n", "*Sparse recovery under weak moment assumptions*\n", "\n", "we proved that reconstruction properties (stability and robustness) of the basis pursuit algorithm goes far beyond Gaussian measurements. For instance, random matrices with i.i.d. components having only $\\log n$ sub-gaussian moments have the same \"reconstruction properties\" has the Gaussian one ($n$ being the size of the signals). \n", "\n", "The aim of this notebook is to highlight this \"universality phenomenum\"." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Random measurements matrices with $\\psi_\\alpha$ coordinates for $0<\\alpha\\leq2$\n", "\n", "We construct matrices with i.i.d. coordinates with exponential moments. Note that if $g$ is a standard Gaussian variable then ${\\rm sign}(g) |g|^{2/\\alpha}$ is exactly a $\\psi_\\alpha$ random variable (with mean zero)." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def mat_exp_power(m, n, alpha):\n", " A = randn(m, n)/ sqrt(m)\n", " return np.multiply(np.power(np.absolute(A),int(2/alpha)), sign(A))" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def phase_transition_mat_exp_power(n, nbiter, gamma, nbtest, alpha):\n", " PTM = zeros((n,int(n/2)))\n", " set_ind_failure = []\n", " for m in range(20,n+1):#construct one line of the Phase transition matrix for a given number of measurements P\n", " A = mat_exp_power(m, n, alpha) \n", " pA = pinv(A) # pseudo-inverse. Equivalent to pA = A.T.dot(inv(A.dot(A.T)))\n", " ind_failure = 0\n", " for sparsity in range(1,min(m, int(n/2))+1):\n", " nb_success = 0 \n", " for i in range(nbtest):\n", " xsharp = signal(n, sparsity)\n", " y = A.dot(xsharp)\n", " x_restored = DR(n, y, A, pA, nbiter, gamma)\n", " if norm(x_restored-xsharp, ord=2) <0.001:\n", " nb_success = nb_success + 1\n", " PTM[m-1, sparsity-1] = nb_success\n", " return PTM" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": true }, "outputs": [], "source": [ "n, nbiter, gamma, nbtest, alpha = 40, 20, 1, 10, 1\n", "mat = phase_transition_mat_exp_power(n, nbiter, gamma, nbtest, alpha)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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a7d/5k77rAh77HY+npXd4tjqh1To6X00CLhlhioJBI/M6+LFrueOd72fxlbu2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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P_min, P_max, S_min, S_max = 0, n, 0, int(n/2)\n", "fig = plt.imshow(mat[P_min:P_max, S_min:S_max], interpolation=\"gaussian\", \n", " aspect='auto', origin = 'lower', extent=[S_min, S_max, P_min, P_max])\n", "titre = \"Psi_alpha measurements for alpha = {}\".format(alpha)\n", "plt.title(titre)\n", "plt.xlabel('sparsity')\n", "plt.ylabel('number of measurements')\n", "\n", "#empirical phase transition\n", "X = range(int(n/2))\n", "L = frontier(mat, n)\n", "plot(X,L, linewidth=4, color = 'black', label='phase transition')\n", "plt.legend(loc=4)\n", "#filename = \"exp_power_{}_{}.png\".format(alpha, n)\n", "#plt.savefig(filename,bbox_inches='tight')" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "power 1.5 running\n", "power 1 running\n", "power 2 running\n", "power 1.8 running\n", "power 0.1 running\n", "power 0.8 running\n", "power 1.2 running\n", "power 0.05 running\n", "power 0.01 running\n", "power 0.5 running\n" ] } ], "source": [ "n, nbiter, gamma, nbtest, nb_curves = 40, 20, 1, 15, 20\n", "L = zeros(int(n/2))\n", "dict_exp_power = {2: L, 1.8: L, 1.5: L, 1.2: L, 1: L, 0.8: L, 0.5: L, 0.1: L, 0.05: L, 0.01: L}\n", "for alpha in dict_exp_power.keys():\n", " print(\"power {} running\".format(alpha))\n", " for i in range(nb_curves): \n", " mat = phase_transition_mat_exp_power(n, nbiter, gamma, nbtest, alpha)\n", " F = frontier(mat, n)\n", " dict_exp_power[alpha] = [sum(a) for a in zip(dict_exp_power[alpha], F)] \n", " dict_exp_power[alpha] = [ele/nb_curves for ele in dict_exp_power[alpha]]" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#save the dictionary of phase transitions curves for later use\n", "import pickle\n", "#To save the dictionary\n", "#with open('dictionnaries_exp_power_100_v3.p', 'wb') as fp:\n", "# pickle.dump(dict_exp_power, fp)\n", " \n", "#to load the dictionary\n", "#n, nbiter, gamma, nbtest, nb_curves = 100, 20, 1, 16, 30\n", "#with open('dictionnaries_exp_power_100_v3.p', 'rb') as fp:\n", "# dict_exp_power = pickle.load(fp)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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DEK+qUsZrOTm7XZ8+SgvJzFRDvPZlnHTDilV2u9ZUDgGCUlLo9bKxvr6REN/s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\nZzP/q1y+WrMaR3QutuwVPL/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nvK4OrF0LU6bAW2/B5Mmdm7kuhpSSjysr+fv27USZTNzX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IeHh5w5c+aGfK6FbT127Ji1beHChVZY1ZCQEHn//fetfWlpadKnTx8REdm5c6cMHTpURESmTJki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\n4b6TfxroWiPNVzXO+TYwFSgFU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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#N = 100\n", "plt.figure(figsize=(8,5))\n", "X = range(int(n/2))\n", "for key in sort(dict_exp_power.keys()):\n", " L = dict_exp_power[key]\n", " text = 'exp power {}'.format(key)\n", " if key == 2:\n", " plot(X, L, 'r--', label = text, linewidth=4)\n", " else:\n", " plot(X, L, label = text)\n", "plt.legend(loc=4)\n", "plt.xlabel('sparsity')\n", "plt.ylabel('number of measurements')\n", "plt.title('phase transition curves -- exponential moments variables')\n", "#plot(X,L_gauss, linewidth=3, color = 'blue', label=\"Gaussian phase transition\")\n", "#plt.legend(loc=4)\n", "#plt.savefig(\"phase_transition_curves_exp_power_100_v3.png\",bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Random measurements matrices with coordinates in $L_p$\n", "For this example, we construct $m\\times n$ i.i.d. Student variables with $k$ degrees of liberty. It has $p$ moments if and only if $k>p$." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def mat_power(m ,n, p):\n", " return random.standard_t(p, size=(m, n))" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def phase_transition_mat_power(n, nbiter, gamma, nbtest, p):\n", " PTM = zeros((n, int(n/2)))\n", " set_ind_failure = []\n", " for m in range(1, n+1):#construct one line of the Phase transition matrix for a given number of measurements P\n", " A = mat_power(m, n, p) \n", " pA = pinv(A) # pseudo-inverse. Equivalent to pA = A.T.dot(inv(A.dot(A.T)))\n", " ind_failure = 0\n", " for sparsity in range(1, min(m, int(n/2))+1):\n", " nb_success = 0 \n", " for i in range(nbtest):\n", " xsharp = signal(n, sparsity)\n", " y = A.dot(xsharp)\n", " x_restored = DR(n, y, A, pA, nbiter, gamma)\n", " if norm(x_restored-xsharp, ord=2) <0.001:\n", " nb_success = nb_success + 1\n", " PTM[m-1, sparsity-1] = nb_success\n", " return PTM" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "power 2 running\n", "power 3 running\n", "power 20 running\n", "power 5 running\n", "power 4 running\n", "power 10 running\n", "power 30 running\n", "power 15 running\n" ] } ], "source": [ "n, nbiter, gamma, nbtest, nb_curves = 30, 20, 1, 10, 20\n", "L = zeros(int(n/2))\n", "dict_power = {30: L, 20: L, 15: L, 10: L, 5: L, 4: L, 3: L, 2: L}\n", "for p in dict_power.keys():\n", " print('power {} running'.format(p))\n", " for i in range(nb_curves):\n", " mat = phase_transition_mat_power(n, nbiter, gamma, nbtest, p)\n", " F = frontier(mat, n)\n", " dict_power[p] = [sum(a) for a in zip(dict_power[p], F)] \n", " dict_power[p] = [ele/nb_curves for ele in dict_power[p]]" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#save the dictionary of phase transitions curves to speed up later investigation\n", "import pickle\n", "#Save the dictionary\n", "#with open('dictionnaries_power_100.p', 'wb') as fp:\n", "# pickle.dump(dict_power, fp)\n", "\n", "#Load the dictionary\n", "#with open('dictionnaries_power_100.p', 'rb') as fp:\n", "# dict_power = pickle.load(fp)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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7D7BsT2VO7knD/nwC4ypU4MXISBxbtcJuzZpbfchCFKvbIbDXBv4AWgNpwBpg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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = range(int(n/2))\n", "plt.figure(figsize=(8,5))\n", "for key in dict_power.keys():\n", " if key != 15:\n", " L = dict_power[key]\n", " text = 'degree {}'.format(key)\n", " plot(X, L, label = text)\n", "plt.xlabel('sparsity')\n", "plt.ylabel('number of measurements')\n", "plt.title('phase transition curves - Student variables')\n", "#Gaussian phase transition\n", "plot(X,L_gauss, 'r--', linewidth=3, label=\"Gaussian phase transition\")\n", "#plt.legend(loc=4)\n", "#plt.savefig(\"phase_transition_curves_student_100.png\",bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Theoretical guarentee on phase transition\n", "\n", "Asymptotically when $n\\to\\infty$, existence of a phase transition, which is roughtly $$m \\geq 2e s \\log\\Big(\\frac{n}{\\sqrt{\\pi}s}\\Big)\\approx 5.4 s \\log\\Big(\\frac{0.6 n}{s}\\Big)$$ has been proved in several papers:\n", ">D. L. Donoho. *High-dimensional centrally symmetric polytopes with neighborliness proportional to dimension.* Discrete and Computational Geometry, 35(4):617–652, 2006.\n", "\n", "> D. L. Donoho and J. Tanner. *Neighborliness of randomly projected simplices in high dimensions.* Proceedings of the National Academy of Sciences of the United States of America, 102(27):9452–9457, 2005.\n", "\n", "> D. L. Donoho and J. Tanner. *Counting faces of randomly projected polytopes when the projection radically lowers dimension.* Journal of the American Mathematical Society, 22(1):1–53, 2009.\n", "\n", ">D. L. Donoho and J. Tanner. *Observed universality of phase transitions in high-dimensional geometry, with implications for modern data analysis and signal processing*. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 367(1906):4273–4293, 2009.\n", "\n", "> S. Oymak and J. A. Tropp. *Universality laws for randomized dimension reduction, with applications*\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }