ROC_analysis_MisMatchedTest_multi(2)_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):\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",
    "    # 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",
    "    KLmm = max(KLmm1, KLmm2)\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",
    "    KLfmm = max(KLfmm1, KLfmm2)\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",
    "    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/4)):\n",
    "        positive_sample[idx] = chain(muP, PP, n)\n",
    "    for idx in range(int(num_test_sample/4), 2 * int(num_test_sample/4)):\n",
    "        positive_sample[idx] = chain(muPP, PPP, n)\n",
    "    \n",
    "    mu = np.reshape(mu, (N, N))\n",
    "    muP = np.reshape(muP, (N, N))\n",
    "    muPP = np.reshape(muPP, (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)\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)\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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DunWqkumRI3WFdED9Zo8YAWlpKpd+yBAASeXBSgqWFVD0UhEZywoQZsHQJUMB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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f297908bcd0>"
      ]
     },
     "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(2)_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": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "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": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}