ROC_analysis_MisMatchedTest_multi(3)_ano_PLs.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import division"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%run util.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data_dir = \"/home/jzh/Dropbox/Research/Anomaly_Detection/MisMatchedTest/\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def KL_est(x, mu, mu1, mu2, mu3):\n",
    "    \"\"\"\n",
    "    Estimate the relative entropy (K-L divergence)\n",
    "    x: a sample path of the chain\n",
    "    mu: the true stationary distribution; an N x N matrix\n",
    "    \"\"\"\n",
    "    mu = np.array(mu)\n",
    "    N, _ = mu.shape\n",
    "    assert(N == _)\n",
    "    \n",
    "    mu1 = np.array(mu1)\n",
    "    N1, _ = mu1.shape\n",
    "    assert(N1 == _)\n",
    "    \n",
    "    mu2 = np.array(mu2)\n",
    "    N2, _ = mu2.shape\n",
    "    assert(N2 == _)\n",
    "    \n",
    "    mu3 = np.array(mu3)\n",
    "    N3, _ = mu3.shape\n",
    "    assert(N3 == _)\n",
    "\n",
    "    # Compute the empirical distribution\n",
    "    eps = 1e-8\n",
    "    gama = [0] * N * N\n",
    "    for j in range(0, N**2):\n",
    "        gama[j] = (x.count(j)) / (len(x))\n",
    "        if gama[j] < eps:\n",
    "            gama[j] = eps\n",
    "    for j in range(0, N**2):\n",
    "        gama[j] = gama[j] / sum(gama)  # Normalize the estimated probability law\n",
    "    gama = np.array(gama)\n",
    "    gama = np.reshape(gama, (N, N))\n",
    "\n",
    "    # Compute the relative entropy (K-L divergence)\n",
    "    d = np.zeros((N, N))\n",
    "    for i in range(0, N):\n",
    "        for j in range(0, N):\n",
    "            d[i, j] = gama[i, j] * (log(gama[i, j] / (sum(gama[i, :]))) - log(mu[i, j] / (sum(mu[i, :]))))\n",
    "    KLht = sum(sum(d))\n",
    "    \n",
    "    # Compute the Mismatched divergence\n",
    "    d = np.zeros((N, N))\n",
    "    for i in range(0, N):\n",
    "        for j in range(0, N):\n",
    "            d[i, j] = gama[i, j] * (log(mu1[i, j] / (sum(mu1[i, :]))) - log(mu[i, j] / (sum(mu[i, :]))))\n",
    "    KLmm1 = sum(sum(d))\n",
    "    \n",
    "    d = np.zeros((N, N))\n",
    "    for i in range(0, N):\n",
    "        for j in range(0, N):\n",
    "            d[i, j] = gama[i, j] * (log(mu2[i, j] / (sum(mu2[i, :]))) - log(mu[i, j] / (sum(mu[i, :]))))\n",
    "    KLmm2 = sum(sum(d))\n",
    "    \n",
    "    d = np.zeros((N, N))\n",
    "    for i in range(0, N):\n",
    "        for j in range(0, N):\n",
    "            d[i, j] = gama[i, j] * (log(mu3[i, j] / (sum(mu3[i, :]))) - log(mu[i, j] / (sum(mu[i, :]))))\n",
    "    KLmm3 = sum(sum(d))\n",
    "    \n",
    "    KLmm = max(KLmm1, KLmm2, KLmm3)\n",
    "\n",
    "    # Compute the \"fake\" Hoeffding relative entropy\n",
    "    d = np.zeros((N, N))\n",
    "    for i in range(0, N):\n",
    "        for j in range(0, N):\n",
    "            d[i, j] = gama[i, j] * (log(gama[i, j]) - log(mu[i, j]))\n",
    "    KLfht = sum(sum(d))\n",
    "    \n",
    "    # Compute the \"fake\" Mismatched divergence\n",
    "    d = np.zeros((N, N))\n",
    "    for i in range(0, N):\n",
    "        for j in range(0, N):\n",
    "            d[i, j] = gama[i, j] * (log(mu1[i, j]) - log(mu[i, j]))\n",
    "    KLfmm1 = sum(sum(d))\n",
    "    \n",
    "    d = np.zeros((N, N))\n",
    "    for i in range(0, N):\n",
    "        for j in range(0, N):\n",
    "            d[i, j] = gama[i, j] * (log(mu2[i, j]) - log(mu[i, j]))\n",
    "    KLfmm2 = sum(sum(d))\n",
    "    \n",
    "    d = np.zeros((N, N))\n",
    "    for i in range(0, N):\n",
    "        for j in range(0, N):\n",
    "            d[i, j] = gama[i, j] * (log(mu3[i, j]) - log(mu[i, j]))\n",
    "    KLfmm3 = sum(sum(d))\n",
    "    \n",
    "    KLfmm = max(KLfmm1, KLfmm2, KLfmm3)\n",
    "\n",
    "    return KLht, KLmm, KLfht, KLfmm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def wcKLs_testSet(N, n, num_test_sample):\n",
    "    # mu_0: the initial distribution; 1 x (N**2) \n",
    "    # mu: the actual stationary distribution; 1 x (N**2)\n",
    "    # mu_1: the estimated stationary distribution \n",
    "    # P: the new transition matrix (the old transition matrix is Q)\n",
    "    # G_1: the estimate of the gradient\n",
    "    # H_1: the estimate of the Hessian\n",
    "\n",
    "    # P is the ground truth transition matrix\n",
    "    mu_0, mu, mu_1, P, G_1, H_1, Sigma_1, W_1, rho_1, Chi_1 = ChainGen(N)  \n",
    "\n",
    "    # PP is a different transition matrix for testing purposes\n",
    "    mu_0P, muP, mu_1P, PP, G_1P, H_1P, Sigma_1P, W_1P, rho_1P, Chi_1P = ChainGen(N) \n",
    "    \n",
    "    # PPP is a further different transition matrix for testing purposes\n",
    "    mu_0PP, muPP, mu_1PP, PPP, G_1PP, H_1PP, Sigma_1PP, W_1PP, rho_1PP, Chi_1PP = ChainGen(N) \n",
    "    \n",
    "    # PPPP is a third different transition matrix for testing purposes\n",
    "    mu_0PPP, muPPP, mu_1PPP, PPPP, G_1PPP, H_1PPP, Sigma_1PPP, W_1PPP, rho_1PPP, Chi_1PPP = ChainGen(N) \n",
    "    \n",
    "    negative_sample = {}\n",
    "    positive_sample = {}\n",
    "\n",
    "    # Get sample paths of the Markov chain with length n; \n",
    "    # these paths will be the test set\n",
    "    for idx in range(int(num_test_sample/2)):\n",
    "        negative_sample[idx] = chain(mu, P, n)\n",
    "    for idx in range(int(num_test_sample/6)):\n",
    "        positive_sample[idx] = chain(muP, PP, n)\n",
    "    for idx in range(int(num_test_sample/6), 2 * int(num_test_sample/6)):\n",
    "        positive_sample[idx] = chain(muPP, PPP, n)\n",
    "    for idx in range(2 * int(num_test_sample/6), 3 * int(num_test_sample/6)):\n",
    "        positive_sample[idx] = chain(muPPP, PPPP, n)\n",
    "    \n",
    "    mu = np.reshape(mu, (N, N))\n",
    "    muP = np.reshape(muP, (N, N))\n",
    "    muPP = np.reshape(muPP, (N, N))\n",
    "    muPPP = np.reshape(muPPP, (N, N))\n",
    "    \n",
    "    # for Hoeffding\n",
    "    negative_sample_KL_HT = {}\n",
    "    positive_sample_KL_HT = {}\n",
    "    \n",
    "    # for Mismatched\n",
    "    negative_sample_KL_MM = {}\n",
    "    positive_sample_KL_MM = {}\n",
    "    \n",
    "    # for \"fake\" Hoeffding\n",
    "    negative_sample_KL_FHT = {}\n",
    "    positive_sample_KL_FHT = {}\n",
    "    \n",
    "    # for \"fake\" Mismatched\n",
    "    negative_sample_KL_FMM = {}\n",
    "    positive_sample_KL_FMM = {}\n",
    "    \n",
    "    # Compute KL divergence values w.r.t. mu for each sample\n",
    "    for idx in range(int(num_test_sample/2)):\n",
    "        negative_sample_KL_HT[idx], negative_sample_KL_MM[idx], negative_sample_KL_FHT[idx], \\\n",
    "        negative_sample_KL_FMM[idx] = KL_est(negative_sample[idx], mu, muP, muPP, muPPP)\n",
    "        \n",
    "    for idx in range(int(num_test_sample/2)):\n",
    "        positive_sample_KL_HT[idx], positive_sample_KL_MM[idx], positive_sample_KL_FHT[idx], \\\n",
    "        positive_sample_KL_FMM[idx] = KL_est(positive_sample[idx], mu, muP, muPP, muPPP)\n",
    "        \n",
    "    return negative_sample_KL_HT, positive_sample_KL_HT, negative_sample_KL_MM, positive_sample_KL_MM, \\\n",
    "negative_sample_KL_FHT, positive_sample_KL_FHT, negative_sample_KL_FMM, positive_sample_KL_FMM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def roc_data(n, beta, num_test_sample, negative_sample_KL_HT, positive_sample_KL_HT, \\\n",
    "             negative_sample_KL_MM, positive_sample_KL_MM, negative_sample_KL_FHT, positive_sample_KL_FHT, \\\n",
    "            negative_sample_KL_FMM, positive_sample_KL_FMM):\n",
    "    \n",
    "    # Get thresholds for Hoeffding's test corresponding to sample length n    \n",
    "    eta = {}\n",
    "    key = str(n) + \"_\" + str(beta)\n",
    "    eta[key] = beta\n",
    "\n",
    "    negative_sample_HT = {}\n",
    "    negative_sample_MM = {}\n",
    "    negative_sample_FHT = {}\n",
    "    negative_sample_FMM = {}\n",
    "\n",
    "    positive_sample_HT = {}\n",
    "    positive_sample_MM = {}\n",
    "    positive_sample_FHT = {}\n",
    "    positive_sample_FMM = {}\n",
    "\n",
    "    for idx in range(int(num_test_sample/2)):\n",
    "        if negative_sample_KL_HT[idx] > eta[key]:\n",
    "            negative_sample_HT[idx] = 1\n",
    "        else:\n",
    "            negative_sample_HT[idx] = -1\n",
    "        if negative_sample_KL_MM[idx] > eta[key]:\n",
    "            negative_sample_MM[idx] = 1\n",
    "        else:\n",
    "            negative_sample_MM[idx] = -1\n",
    "        if negative_sample_KL_FHT[idx] > eta[key]:\n",
    "            negative_sample_FHT[idx] = 1\n",
    "        else:\n",
    "            negative_sample_FHT[idx] = -1\n",
    "        if negative_sample_KL_FMM[idx] > eta[key]:\n",
    "            negative_sample_FMM[idx] = 1\n",
    "        else:\n",
    "            negative_sample_FMM[idx] = -1\n",
    "\n",
    "\n",
    "    for idx in range(int(num_test_sample/2)):\n",
    "        if positive_sample_KL_HT[idx] > eta[key]:\n",
    "            positive_sample_HT[idx] = 1\n",
    "        else:\n",
    "            positive_sample_HT[idx] = -1\n",
    "        if positive_sample_KL_MM[idx] > eta[key]:\n",
    "            positive_sample_MM[idx] = 1\n",
    "        else:\n",
    "            positive_sample_MM[idx] = -1\n",
    "        if positive_sample_KL_FHT[idx] > eta[key]:\n",
    "            positive_sample_FHT[idx] = 1\n",
    "        else:\n",
    "            positive_sample_FHT[idx] = -1\n",
    "        if positive_sample_KL_FMM[idx] > eta[key]:\n",
    "            positive_sample_FMM[idx] = 1\n",
    "        else:\n",
    "            positive_sample_FMM[idx] = -1\n",
    "            \n",
    "\n",
    "    TP_HT = count_one(positive_sample_HT.values())[0]\n",
    "    FP_HT = count_one(negative_sample_HT.values())[0]\n",
    "    TN_HT = count_one(negative_sample_HT.values())[1]\n",
    "    FN_HT = count_one(positive_sample_HT.values())[1]\n",
    "    TPR_HT = TP_HT / (TP_HT + FN_HT)\n",
    "    FPR_HT = FP_HT / (FP_HT + TN_HT)\n",
    "\n",
    "    TP_MM = count_one(positive_sample_MM.values())[0]\n",
    "    FP_MM = count_one(negative_sample_MM.values())[0]\n",
    "    TN_MM = count_one(negative_sample_MM.values())[1]\n",
    "    FN_MM = count_one(positive_sample_MM.values())[1]\n",
    "    TPR_MM = TP_MM / (TP_MM + FN_MM)\n",
    "    FPR_MM = FP_MM / (FP_MM + TN_MM)\n",
    "    \n",
    "    TP_FHT = count_one(positive_sample_FHT.values())[0]\n",
    "    FP_FHT = count_one(negative_sample_FHT.values())[0]\n",
    "    TN_FHT = count_one(negative_sample_FHT.values())[1]\n",
    "    FN_FHT = count_one(positive_sample_FHT.values())[1]\n",
    "    TPR_FHT = TP_FHT / (TP_FHT + FN_FHT)\n",
    "    FPR_FHT = FP_FHT / (FP_FHT + TN_FHT)\n",
    "    \n",
    "    TP_FMM = count_one(positive_sample_FMM.values())[0]\n",
    "    FP_FMM = count_one(negative_sample_FMM.values())[0]\n",
    "    TN_FMM = count_one(negative_sample_FMM.values())[1]\n",
    "    FN_FMM = count_one(positive_sample_FMM.values())[1]\n",
    "    TPR_FMM = TP_FMM / (TP_FMM + FN_FMM)\n",
    "    FPR_FMM = FP_FMM / (FP_FMM + TN_FMM)\n",
    "    \n",
    "    data_HT = {\"TPR\": TPR_HT, \"FPR\":FPR_HT}\n",
    "    data_MM = {\"TPR\": TPR_MM, \"FPR\":FPR_MM}\n",
    "    data_FHT = {\"TPR\": TPR_FHT, \"FPR\":FPR_FHT}\n",
    "    data_FMM = {\"TPR\": TPR_FMM, \"FPR\":FPR_FMM}\n",
    "    \n",
    "    return data_HT, data_MM, data_FHT, data_FMM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "N = 3\n",
    "n = 20\n",
    "num_test_sample = 12000\n",
    "\n",
    "beta_list = list(np.arange(-2, 2, 0.0001)[1:-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# beta_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<string>:332: RuntimeWarning: covariance is not positive-semidefinite.\n"
     ]
    }
   ],
   "source": [
    "negative_sample_KL_HT, positive_sample_KL_HT, negative_sample_KL_MM, positive_sample_KL_MM, \\\n",
    "negative_sample_KL_FHT, positive_sample_KL_FHT, negative_sample_KL_FMM, positive_sample_KL_FMM = \\\n",
    "wcKLs_testSet(N, n, num_test_sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# negative_sample_KL_MM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "roc_data_HT = {}\n",
    "roc_data_MM = {}\n",
    "roc_data_FHT = {}\n",
    "roc_data_FMM = {}\n",
    "\n",
    "for beta in beta_list:\n",
    "    roc_data_HT[beta], roc_data_MM[beta], roc_data_FHT[beta], roc_data_FMM[beta] = \\\n",
    "    roc_data(n, beta, num_test_sample, negative_sample_KL_HT, positive_sample_KL_HT, \\\n",
    "             negative_sample_KL_MM, positive_sample_KL_MM, negative_sample_KL_FHT, positive_sample_KL_FHT, \\\n",
    "            negative_sample_KL_FMM, positive_sample_KL_FMM)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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HJtbuX8vTlz9NkDWI1656DbPJjD3cDsC0ftOY1m9a+9yrEEIaAOIYp9OYdfX6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\nEu745vN446UpTOyewKHCZezadhs+8oWD4y4eUV8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Ynp5uGJsHBjsPAN000tsApZS2EMIS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\nKxgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbc58c7df10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import pylab\n",
    "from pylab import *\n",
    "%matplotlib inline  \n",
    "import itertools \n",
    "\n",
    "\n",
    "plt.figure(figsize=(8, 4))\n",
    "\n",
    "font = {\"family\" : \"normal\",\n",
    "        \"weight\" : \"normal\",\n",
    "        \"size\"   : 18}\n",
    "\n",
    "matplotlib.rc('font', **font)\n",
    "\n",
    "from matplotlib import rc\n",
    "# rc('font',**{'family':'sans-serif','sans-serif':['Helvetica']})\n",
    "# ## for Palatino and other serif fonts use:\n",
    "# #rc('font',**{'family':'serif','serif':['Palatino']})\n",
    "rc('text', usetex=True)\n",
    "\n",
    "roc_HT_re, = plt.plot([roc_data_HT[beta][\"FPR\"] for beta in beta_list], \\\n",
    "                     [roc_data_HT[beta][\"TPR\"] for beta in beta_list], \"r-.\", linewidth=1.5, markersize=5, \\\n",
    "                        markerfacecolor=\"None\", markeredgecolor=\"r\", markeredgewidth=1)\n",
    "\n",
    "roc_MM_re, = plt.plot([roc_data_MM[beta][\"FPR\"] for beta in beta_list], \\\n",
    "                     [roc_data_MM[beta][\"TPR\"] for beta in beta_list], \"b-\", linewidth=1.5, markersize=5, \\\n",
    "                        markerfacecolor=\"None\", markeredgecolor=\"b\", markeredgewidth=1)\n",
    "\n",
    "roc_FHT_re, = plt.plot([roc_data_FHT[beta][\"FPR\"] for beta in beta_list], \\\n",
    "                     [roc_data_FHT[beta][\"TPR\"] for beta in beta_list], \"g:\", linewidth=1.5, markersize=5, \\\n",
    "                        markerfacecolor=\"None\", markeredgecolor=\"g\", markeredgewidth=1)\n",
    "\n",
    "roc_FMM_re, = plt.plot([roc_data_FMM[beta][\"FPR\"] for beta in beta_list], \\\n",
    "                     [roc_data_FMM[beta][\"TPR\"] for beta in beta_list], \"m--\", linewidth=1.5, markersize=5, \\\n",
    "                        markerfacecolor=\"None\", markeredgecolor=\"b\", markeredgewidth=1)\n",
    "\n",
    "legend_list = [r\"Hoeffding Test\", r\"Mismatched Test\", r\"``Faked'' Hoeffding Test\", r\"``Faked'' Mismatched Test\"]\n",
    "\n",
    "# legend(loc=0, fancybox=\"true\", ncol=2, mode=\"expand\", borderaxespad=0.2) \n",
    "\n",
    "plt.legend([roc_HT_re, roc_MM_re, roc_FHT_re, roc_FMM_re,], legend_list, loc=4, numpoints=1, \\\n",
    "           fancybox=\"false\", frameon=False) \n",
    "plt.title(r\"$N = %s, n = %s$\"%(N, n))\n",
    "# plt.xticks(N_list)\n",
    "\n",
    "pylab.xlim(-0.02, 1.02)\n",
    "pylab.ylim(-0.02, 1.02)\n",
    "\n",
    "plt.xlabel(\"FPR\")\n",
    "plt.ylabel(\"TPR\")\n",
    "# plt.grid()\n",
    "\n",
    "savefig(data_dir + \"ROC_N_%s_n_%s_multi(3)_ano_PLs.eps\"%(N, n), dpi=300, bbox_inches=\"tight\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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