known-pos-vs-known-neg-python3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Importance of known positives versus known negatives\n",
    "\n",
    "In this notebook we will show how to compute performance curves (ROC and PR curves to be specific) based on a data set with known positives, known negatives and unlabeled data. We will show how to use our approach starting from known negatives instead of known positives, which is useful of the number of known negatives is much larger.\n",
    "\n",
    "This notebook is intended to enable you to easily change the configuration of experiments, so feel free to make modifications where you see fit to see their effect."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import operator as op\n",
    "import optunity.metrics\n",
    "import semisup_metrics as ss\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "import pickle\n",
    "import csv\n",
    "import util\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Create or load data set\n",
    "Generate simulated data. Feel free to configure the code below as you please."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# fraction of positives/negatives that are known\n",
    "# known_neg_frac == 0 implies PU learning\n",
    "known_pos_frac = 0.05\n",
    "known_neg_frac = 0.5\n",
    "\n",
    "# if you simulate a smaller data set you can see some effects better\n",
    "# but estimated bounds will be much wider\n",
    "# because the ECDF confidence interval becomes large\n",
    "num_pos = 10000  \n",
    "num_neg = 10000 \n",
    "distid = 2  # can be 1, 2 or 3, these correspond to certain curves in ROC space\n",
    "\n",
    "# generate rankings and label vectors and compute corresponding beta\n",
    "# beta is based on known_pos_frac, known_neg_frac and the number of pos and negs\n",
    "# labels is a list of {True, False, None}, where None indicates unlabeled\n",
    "# true_labels is a list of {True, False}\n",
    "labels, true_labels, decision_values, beta = util.simulate_data(distid, num_pos, num_neg,\n",
    "                                                                known_pos_frac,\n",
    "                                                                known_neg_frac)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data set characteristics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Known parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total number of instances: \t 20000\n",
      "number of known positives: \t 500\n",
      "number of known negatives: \t 5000\n",
      "number of unlabeled instances: \t 14500\n"
     ]
    }
   ],
   "source": [
    "print('total number of instances: \\t %d' % len(labels))\n",
    "print('number of known positives: \\t %d' % len(list(filter(lambda x: x == True, labels))))\n",
    "print('number of known negatives: \\t %d' % len(list(filter(lambda x: x == False, labels))))\n",
    "print('number of unlabeled instances: \\t %d' % len(list(filter(lambda x: x == None, labels))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unknown parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of latent positives: \t 9500\n",
      "number of latent negatives: \t 5000\n",
      "beta: \t 0.6552\n"
     ]
    }
   ],
   "source": [
    "print('number of latent positives: \\t %d' % len(list(filter(lambda x: x[0] == None and x[1] == True, zip(labels, true_labels)))))\n",
    "print('number of latent negatives: \\t %d' % len(list(filter(lambda x: x[0] == None and x[1] == False, zip(labels, true_labels)))))\n",
    "print('beta: \\t %1.4f' % beta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Estimate beta\n",
    "\n",
    "As this notebook is intended to show the effect of known positives vs known negatives, we will continue with the true value of beta. Change this parameter to see its effect in the figures later on."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "true value of beta\t0.6552\n",
      "point estimate of beta\t0.6552\n"
     ]
    }
   ],
   "source": [
    "betahat = beta\n",
    "\n",
    "print('true value of beta\\t%1.4f' % beta)\n",
    "print('point estimate of beta\\t%1.4f' % betahat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Compute cumulative rank distribution of known positives\n",
    "\n",
    "We start by computing the rank CDF of known positives, and then determine a confidence interval for it. We will use a standard bootstrap approach."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# sort the labels in descending order of corresponding decision values\n",
    "sort_labels, sort_dv, sort_true_labels = zip(*sorted(zip(labels, decision_values, true_labels),\n",
    "                                                     key=op.itemgetter(1), reverse=True))\n",
    "\n",
    "# ranks of the known positives\n",
    "known_pos_ranks = [idx for idx, lab in enumerate(sort_labels) if lab]\n",
    "\n",
    "# compute rank ECDF of known positives\n",
    "known_pos_ecdf = ss.compute_ecdf_curve(known_pos_ranks)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we determine a confidence interval on the rank CDF of known positives. We can do this in several ways, our code provides a bootstrap approach and a method based on the Dvoretzky–Kiefer–Wolfowitz (DKW) inequality. Feel free to experiment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "ci_width = 0.95      # width of the confidence band on ECDF to be used\n",
    "use_bootstrap = True # use bootstrap to compute confidence band\n",
    "nboot = 2000         # number of bootstrap iterations to use, not used if use_bootstrap = False\n",
    "\n",
    "if use_bootstrap:\n",
    "    pos_cdf_bounds = ss.bootstrap_ecdf_bounds(labels, decision_values, nboot=nboot, ci_width=ci_width)\n",
    "else:\n",
    "    pos_cdf_bounds = ss.dkw_bounds(labels, decision_values, ci_width=ci_width)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For reference, we will also compute the rank ECDF of latent positives. In practical applications this is impossible, as the latent positives are by definition not known."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "latent_positives = map(lambda x, y: x == True and y == None, true_labels, labels)\n",
    "sort_lps, _ = zip(*sorted(zip(latent_positives, decision_values),\n",
    "                          key=op.itemgetter(1), reverse=True))\n",
    "latent_pos_ranks = [idx for idx, lab in enumerate(sort_lps) if lab]\n",
    "latent_pos_ecdf = ss.compute_ecdf_curve(latent_pos_ranks)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the rank CDFs of known and latent positives. It may occur that the rank CDF of latent positives is not within the confidence interval of known positives, in which case the corresponding bounds on performance will not be strict."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# convenience plot functions\n",
    "def plot_proxy(color, alpha):\n",
    "    p = plt.Rectangle((0, 0), 0, 0, color=color, alpha=alpha)\n",
    "    ax = plt.gca()\n",
    "    ax.add_patch(p)\n",
    "    return p\n",
    "\n",
    "def fix_plot_shape(fig):\n",
    "    ax = fig.add_subplot(111, aspect='equal')\n",
    "    axes = fig.gca()\n",
    "    axes.set_xlim([0,1])\n",
    "    axes.set_ylim([0,1])\n",
    "\n",
    "xs = list(range(len(labels)))\n",
    "plt.figure(1)\n",
    "plt.fill_between(xs, list(map(pos_cdf_bounds.lower, xs)), list(map(pos_cdf_bounds.upper, xs)), \n",
    "                 color='blue', alpha=0.4)\n",
    "plt.plot(*zip(*known_pos_ecdf), color='black', linestyle='dashed', linewidth=2)\n",
    "plt.plot(*zip(*latent_pos_ecdf), color='black', linewidth=2)\n",
    "plot_proxy('blue', 0.4)\n",
    "plt.xlabel('rank')\n",
    "plt.ylabel('TPR')\n",
    "plt.legend(['known positives', 'latent positives', 'expected region'], loc=4)\n",
    "plt.title('Rank CDF')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Compute cumulative rank distribution of known negatives\n",
    "\n",
    "The code below is analogous to what we did earlier for known positives, but now for known negatives. We will first flip known class labels, as described in the text."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ranks of the known positives\n",
    "known_neg_ranks = [idx for idx, lab in enumerate(sort_labels) if lab == False]\n",
    "\n",
    "# compute rank ECDF of known positives\n",
    "known_neg_ecdf = ss.compute_ecdf_curve(sorted(known_neg_ranks))\n",
    "\n",
    "# flip class labels\n",
    "labels_flipped = [not label if label is not None else None for label in labels]\n",
    "sort_labels_flipped = [not label if label is not None else None for label in sort_labels]\n",
    "\n",
    "# compute confidence interval in the same way as we did for known positives\n",
    "if use_bootstrap:\n",
    "    neg_cdf_bounds = ss.bootstrap_ecdf_bounds(labels_flipped, decision_values, nboot=nboot, ci_width=ci_width)\n",
    "else:\n",
    "    neg_cdf_bounds = ss.dkw_bounds(labels_flipped, decision_values, ci_width=ci_width)\n",
    "    \n",
    "# for reference, rank CDF of latent negatives\n",
    "latent_negatives = map(lambda x, y: x == False and y == None, true_labels, labels)\n",
    "sort_lns, _ = zip(*sorted(zip(latent_negatives, decision_values),\n",
    "                          key=op.itemgetter(1), reverse=True))\n",
    "latent_neg_ranks = [idx for idx, lab in enumerate(sort_lns) if lab]\n",
    "latent_neg_ecdf = ss.compute_ecdf_curve(latent_neg_ranks)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot rank CDFs of known positives and known negatives along with their CIs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = list(range(len(labels)))\n",
    "plt.figure(1)\n",
    "plt.fill_between(xs, list(map(pos_cdf_bounds.lower, xs)), list(map(pos_cdf_bounds.upper, xs)), \n",
    "                 color='blue', alpha=0.4)\n",
    "plt.plot(*zip(*known_pos_ecdf), color='blue', linestyle='dashed', linewidth=2)\n",
    "plt.plot(*zip(*latent_pos_ecdf), color='blue', linewidth=2)\n",
    "plot_proxy('blue', 0.4)\n",
    "\n",
    "plt.fill_between(xs, list(map(neg_cdf_bounds.lower, xs)), list(map(neg_cdf_bounds.upper, xs)), \n",
    "                 color='red', alpha=0.4)\n",
    "plt.plot(*zip(*known_neg_ecdf), color='red', linestyle='dashed', linewidth=2)\n",
    "plt.plot(*zip(*latent_neg_ecdf), color='red', linewidth=2)\n",
    "plot_proxy('red', 0.4)\n",
    "plt.xlabel('rank')\n",
    "plt.ylabel('TPR')\n",
    "plt.legend(['known positives', 'latent positives', 'known negatives', 'latent negatives', 'CI for pos', 'CI for neg'], \n",
    "           loc=\"upper left\", bbox_to_anchor=(1,1))\n",
    "plt.title('Rank CDF')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Compute contingency tables for each rank\n",
    "We will compute contingency tables based on the rank distribution of known positives and based on the rank distribution of known negatives.\n",
    "\n",
    "Applying our approach to known negatives requires a few modifications:\n",
    "1. Flip known class labels, so negatives become positives\n",
    "2. Modify beta (new beta = 1 - beta)\n",
    "3. Run our approach\n",
    "4. Adjust resulting contingency tables (i.e., flip class labels back). Note also that the optimistic contingency table becomes the pessimistic table when flipping labels and vice versa."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# compute contingency tables based on CI of rank CDF of known positives\n",
    "tables_pos = ss.compute_contingency_tables(labels=sort_labels, decision_values=sort_dv,\n",
    "                                             reference_lb=pos_cdf_bounds.lower,\n",
    "                                             reference_ub=pos_cdf_bounds.upper,\n",
    "                                             beta=betahat, presorted=True)\n",
    "\n",
    "# compute contingency tables based on CI of rank CDF of known negatives\n",
    "# this requires flipping labels, changing beta and post-processing the resulting contingency tables\n",
    "betahat_flipped = 1.0 - betahat\n",
    "tables_neg = ss.compute_contingency_tables(labels=sort_labels_flipped, decision_values=sort_dv,\n",
    "                                           reference_lb=neg_cdf_bounds.lower,\n",
    "                                           reference_ub=neg_cdf_bounds.upper,\n",
    "                                           beta=betahat_flipped, presorted=True)\n",
    "postprocess_ct = lambda ct: ss.ContingencyTable(TP=ct.FP,\n",
    "                                                FP=ct.TP,\n",
    "                                                TN=ct.FN,\n",
    "                                                FN=ct.TN)\n",
    "tables_neg_post = ss._lb_ub(lower=list(map(postprocess_ct, tables_neg.upper)),\n",
    "                            upper=list(map(postprocess_ct, tables_neg.lower)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4. Compute and plot performance estimates based on the contingency tables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.1 ROC curves\n",
    "\n",
    "Start off with the easy stuff: the true ROC curve (unknown in practice), and the curve we obtain by assuming beta=0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# compute the true ROC curve (we use Optunity's ROC function)\n",
    "_, roc_true = optunity.metrics.roc_auc(true_labels, decision_values, return_curve=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute bounds based on the proposed method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# we can directly use the contingency tables we already computed anyways\n",
    "roc_bounds = lambda tables: ss._lb_ub(lower=ss.roc_from_cts(tables.lower),\n",
    "                                      upper=ss.roc_from_cts(tables.upper))\n",
    "\n",
    "# bounds starting from known positives\n",
    "roc_bounds_pos = roc_bounds(tables_pos)\n",
    "\n",
    "# bounds starting from known negatives\n",
    "roc_bounds_neg = roc_bounds(tables_neg_post)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the resulting curves"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = [float(x) / 100 for x in range(101)]\n",
    "roc_pos_up = ss.zoh(*zip(*roc_bounds_pos.upper))\n",
    "roc_pos_lo = ss.zoh(*zip(*roc_bounds_pos.lower))\n",
    "roc_neg_up = ss.zoh(*zip(*roc_bounds_neg.upper))\n",
    "roc_neg_lo = ss.zoh(*zip(*roc_bounds_neg.lower))\n",
    "fig = plt.figure(2)\n",
    "fix_plot_shape(fig)\n",
    "plt.plot(*zip(*roc_true), color='black', linewidth=2)\n",
    "plt.fill_between(xs, list(map(roc_pos_lo, xs)), list(map(roc_pos_up, xs)), color='blue', alpha=0.3)\n",
    "plt.fill_between(xs, list(map(roc_neg_lo, xs)), list(map(roc_neg_up, xs)), color='red', alpha=0.7)\n",
    "plot_proxy('blue', 0.3)\n",
    "plot_proxy('red', 0.7)\n",
    "plt.xlabel('FPR')\n",
    "plt.ylabel('TPR')\n",
    "plt.legend(['true curve', 'expected region via known pos', 'expected region via known neg'],\n",
    "           loc=\"upper left\", bbox_to_anchor=(1,1))\n",
    "plt.title('Receiver Operating Characteristic curve')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The resulting curves show clearly that in this case computing bounds based on known negatives is better, because we have far more known negatives."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.2 PR curves"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# we can directly use the contingency tables we already computed anyways\n",
    "pr_bounds = lambda tables: ss._lb_ub(lower=ss.pr_from_cts(tables.lower),\n",
    "                                     upper=ss.pr_from_cts(tables.upper))\n",
    "pr_bounds_pos = pr_bounds(tables_pos)\n",
    "pr_bounds_neg = pr_bounds(tables_neg_post)\n",
    "\n",
    "# an alternative without all these intermediate steps would be:\n",
    "# roc_bounds_point = ss.roc_bounds(labels, decision_values, beta=betahat)\n",
    "\n",
    "# compute the true ROC curve (we use Optunity's ROC function)\n",
    "_, pr_true = optunity.metrics.pr_auc(true_labels, decision_values, return_curve=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pr_pos_up = ss.zoh(*zip(*pr_bounds_pos.upper))\n",
    "pr_pos_lo = ss.zoh(*zip(*pr_bounds_pos.lower))\n",
    "pr_neg_up = ss.zoh(*zip(*pr_bounds_neg.upper))\n",
    "pr_neg_lo = ss.zoh(*zip(*pr_bounds_neg.lower))\n",
    "fig = plt.figure(3)\n",
    "fix_plot_shape(fig)\n",
    "plt.plot(*zip(*pr_true), color='black', linewidth=2)\n",
    "plt.fill_between(xs, list(map(pr_pos_lo, xs)), list(map(pr_pos_up, xs)), color='blue', alpha=0.3)\n",
    "plt.fill_between(xs, list(map(pr_neg_lo, xs)), list(map(pr_neg_up, xs)), color='red', alpha=0.7)\n",
    "plot_proxy('blue', 0.3)\n",
    "plot_proxy('red', 0.7)\n",
    "plt.xlabel('Recall')\n",
    "plt.ylabel('Precision')\n",
    "plt.legend(['true curve', 'expected region via known pos', 'expected region via known neg'],\n",
    "           loc=\"upper left\", bbox_to_anchor=(1,1))\n",
    "plt.title('Precision-Recall curve')\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}