Mixed data.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import seaborn as sns\n",
    "from matplotlib import pyplot as plt\n",
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_sample(n = 1000, m = 5):\n",
    "    X = []\n",
    "    Y = []\n",
    "    for i in range(n):\n",
    "        y = random.randint(0, m - 1)\n",
    "        x = np.random.uniform(y, y + 2)\n",
    "        X.append(x)\n",
    "        Y.append(y)\n",
    "    return np.array(X).reshape(-1, 1), np.array(Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, y = get_sample(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x115f24da0>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9626301024966701"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.ensemble.forest import _generate_unsampled_indices\n",
    "from sklearn.ensemble import BaggingClassifier\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "import math\n",
    "\n",
    "\n",
    "def cef_estimate(X, y, n_estimators = 200, max_samples = .32, bootstrap = True, depth = 30, min_samples_leaf = 1, max_features = 1.):\n",
    "    model = BaggingClassifier(DecisionTreeClassifier(max_depth = depth, min_samples_leaf = min_samples_leaf, max_features = math.ceil(int(math.sqrt(X.shape[1])))), \n",
    "                              n_estimators = n_estimators, \n",
    "                              max_samples= max_samples, \n",
    "                              bootstrap = bootstrap)\n",
    "    model.fit(X, y)\n",
    "    class_counts = np.zeros((X.shape[0], model.n_classes_))\n",
    "    for tree in model:\n",
    "        # get out of bag indicies\n",
    "        unsampled_indices = _generate_unsampled_indices(tree.random_state, len(X))\n",
    "        \n",
    "        total_unsampled = len(unsampled_indices)\n",
    "        np.random.shuffle(unsampled_indices)\n",
    "        prob_indices, eval_indices = unsampled_indices[:total_unsampled//2], unsampled_indices[total_unsampled//2:]\n",
    "        # get all node counts\n",
    "        node_counts = tree.tree_.n_node_samples\n",
    "        # get probs for eval samples\n",
    "        posterior_class_counts = np.zeros((len(node_counts), model.n_classes_))\n",
    "        for prob_index in prob_indices:\n",
    "            posterior_class_counts[tree.apply(X[prob_index].reshape(1, -1)).item(), y[prob_index]] += 1\n",
    "        row_sums = posterior_class_counts.sum(axis=1)\n",
    "        row_sums[row_sums == 0] = 1\n",
    "        class_probs = (posterior_class_counts/row_sums[:, None])\n",
    "        where_0 = np.argwhere(class_probs == 0)\n",
    "        for elem in where_0:\n",
    "            class_probs[elem[0], elem[1]] = 1/(model.n_classes_*row_sums[elem[0], None])\n",
    "        where_1 = np.argwhere(class_probs == 1)\n",
    "        for elem in where_1:\n",
    "            class_probs[elem[0], elem[1]] = 1 - (model.n_classes_ - 1)/(model.n_classes_*row_sums[elem[0], None])\n",
    "        class_probs.tolist()\n",
    "        partition_counts = np.asarray([node_counts[x] for x in tree.apply(X[eval_indices])])\n",
    "        # get probability for out of bag samples\n",
    "        eval_class_probs = [class_probs[x] for x in tree.apply(X[eval_indices])]\n",
    "        eval_class_probs = np.array(eval_class_probs)\n",
    "        # find total elements for out of bag samples\n",
    "        elems = np.multiply(eval_class_probs, partition_counts[:, np.newaxis])\n",
    "        # store counts for each x (repeat fhis for each tree)\n",
    "        class_counts[eval_indices] += elems\n",
    "    # calculate p(y|X = x) for all x's\n",
    "    probs = class_counts/class_counts.sum(axis = 1, keepdims = True)\n",
    "    entropies = -np.sum(np.log(probs)*probs, axis = 1)\n",
    "    # convert nan to 0\n",
    "    entropies = np.nan_to_num(entropies)\n",
    "    return np.mean(entropies)\n",
    "\n",
    "np.warnings.filterwarnings('ignore')\n",
    "\n",
    "from scipy.stats import entropy\n",
    "\n",
    "def get_entropy(X):\n",
    "    probs = np.bincount(X)/len(X)\n",
    "    return entropy(probs)\n",
    "\n",
    "def get_mutual_information(X, y, n_estimators = 300, max_samples = .32, depth = 30):\n",
    "    cond_entropy = cef_estimate(X, y, n_estimators = n_estimators, max_samples = max_samples, depth = depth)\n",
    "    h_y = get_entropy(y)\n",
    "    return h_y - cond_entropy\n",
    "X, y = get_sample(30000, 5)\n",
    "get_mutual_information(X, y)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mixed.Mixed_KSG(X, y.reshape(-1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "from tqdm import tqdm_notebook\n",
    "import sys\n",
    "sys.path.insert(0, \"./code\")\n",
    "import entropy_estimators as ee\n",
    "import mixed\n",
    "\n",
    "def mutual_information_v_n(m = 2):\n",
    "    sample_sizes = [i*50 for i in range(1, 51)]\n",
    "\n",
    "    cef = []\n",
    "    kraskov = []\n",
    "    mixed_ksg = []\n",
    "    for n in tqdm_notebook(sample_sizes):\n",
    "        X, y = get_sample(n, m)\n",
    "        h_y = get_entropy(y)\n",
    "        kraskov.append(ee.micd(X, y.reshape(-1, 1)))\n",
    "        cef.append(get_mutual_information(X, y)/h_y)\n",
    "        mixed_ksg.append(mixed.Mixed_KSG(X, y.reshape(-1, 1))/h_y)\n",
    "    return sample_sizes, cef, kraskov, mixed_ksg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#sample_sizes, cef, kraskov, mixed_ksg = mutual_information_v_n(5)\n",
    "sns.set(font_scale = 3.5)\n",
    "sns.set_style(\"ticks\")\n",
    "plt.figure()\n",
    "plt.rcParams[\"font.family\"] = \"sans-serif\"\n",
    "plt.rcParams['figure.figsize'] = [15, 10]\n",
    "\n",
    "plt.plot(sample_sizes, cef, label = \"CF\", linewidth = 2, color = \"#F41711\")\n",
    "plt.plot(sample_sizes, kraskov, label = \"KSG\", linewidth = 2, color = \"#35978f\")\n",
    "plt.plot(sample_sizes, mixed_ksg, label = \"Mixed KSG\", linewidth = 2, color = \"#fdae61\")\n",
    "\n",
    "\n",
    "line_true = plt.axhline(y=.65,linestyle='-', color = \"black\", label = \"Truth\")\n",
    "\n",
    "plt.xlabel(\"Sample Size\")\n",
    "plt.ylabel(\"Normalized MI\")\n",
    "plt.ylim(ymin = 0)\n",
    "plt.ylim(ymax = .8)\n",
    "plt.yticks(fontsize=30)\n",
    "plt.xticks(fontsize=30)\n",
    "#plt.legend()\n",
    "#plt.title(\"H(Y|X) Estimate vs Sample Size with Mean = 1\")\n",
    "plt.tight_layout()\n",
    "plt.savefig(\"mi_mixed_m_5.pdf\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.973163418758083, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]\n"
     ]
    }
   ],
   "source": [
    "print(cef)"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "log(m) − (m − 1)log(2)/m\n",
    "\n",
    "\n",
    "log(m) − (m − 1)log(2)/m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, y = get_sample(100000,  m = 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6931392603390353"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_entropy(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}