Algorithm revised.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "%matplotlib inline\n",
    "\n",
    "# NOTE: we are storing y's as 1's or 0's but still doing the mean stuff correctly\n",
    "def get_sample(n, mean, var):\n",
    "    x_sample = []\n",
    "    y_sample = []\n",
    "    for i in range(n):\n",
    "        y = np.random.binomial(1, .5)\n",
    "        if (y == 0):\n",
    "            x = np.random.normal(-mean, var)\n",
    "        else:\n",
    "            x = np.random.normal(mean, var)\n",
    "        x_sample.append(x)\n",
    "        y_sample.append(y)\n",
    "    return x_sample, y_sample\n",
    "\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "def split_by_class(sample):\n",
    "    y_one = [pair for pair in sample if pair[1] == 1]\n",
    "    y_neg_one = [pair for pair in sample if pair[1] == 0]\n",
    "    return y_one, y_neg_one\n",
    "\n",
    "X, y = get_sample(5000, 2, 1)\n",
    "sample = list(zip(X, y))\n",
    "class_two, class_neg_two = split_by_class(sample)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11138a710>"
      ]
     },
     "execution_count": 2,
     "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": [
    "sns.set(font_scale = 2.5)\n",
    "sns.set_style(\"ticks\")\n",
    "plt.rcParams[\"font.family\"] = \"sans-serif\"\n",
    "plt.rcParams['figure.figsize'] = [15, 10]\n",
    "plt.rcParams['lines.linewidth'] = 3\n",
    "plt.figure()\n",
    "\n",
    "sns.distplot(list(zip(*class_two))[0], hist=False, color = \"#1b9e77\", label = u'\\u03bc = 0')\n",
    "sns.distplot(list(zip(*class_neg_two))[0], hist=False, color = \"#1b9e77\", label = u'\\u03bc = 0')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.ensemble.forest import _generate_unsampled_indices\n",
    "from sklearn.ensemble import BaggingClassifier\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.model_selection import train_test_split\n",
    "import math\n",
    "\n",
    "\n",
    "def rf_entropy_estimate_bagging_revised(X, y, n_estimators = 300, nu = .33, bootstrap = True, depth = 30, min_samples_leaf = 1, max_features = 1.):\n",
    "    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=nu, random_state=42)\n",
    "    \n",
    "    max_samples = int(len(X_train)*.5)\n",
    "    split_samples = max_samples // 2\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= split_samples, \n",
    "                              bootstrap = bootstrap)\n",
    "    model.fit(X_train, y_train)\n",
    "    class_counts = np.zeros((X_test.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 = unsampled_indices[:split_samples]\n",
    "\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 unsampled_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",
    "        \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",
    "        \n",
    "        class_probs.tolist()\n",
    "        partition_counts = np.asarray([node_counts[x] for x in tree.apply(X_test)])\n",
    "        # get probability for out of bag samples\n",
    "        eval_class_probs = [class_probs[x] for x in tree.apply(X_test)]\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 += elems\n",
    "    # calculate p(y|X = x) for all x's\n",
    "    probs = class_counts/class_counts.sum(axis = 1, keepdims = True)\n",
    "    print(probs)\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",
    "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 = 1000):\n",
    "    cond_entropy = rf_entropy_estimate_bagging_revised(X, y, n_estimators = n_estimators)\n",
    "    h_y = get_entropy(y)\n",
    "    return h_y - cond_entropy\n",
    "\n",
    "\n",
    "np.warnings.filterwarnings('ignore')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, y = get_sample(10000, 1, 1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.93941421 0.06058579]\n",
      " [0.51563283 0.48436717]\n",
      " [0.90314562 0.09685438]\n",
      " ...\n",
      " [0.03828684 0.96171316]\n",
      " [0.99277368 0.00722632]\n",
      " [0.27080453 0.72919547]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.33212108770818055"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rf_entropy_estimate_bagging_revised(np.array(X).reshape(-1, 1), y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3539784023963846"
      ]
     },
     "execution_count": 11,
     "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 rf_entropy_estimate_bagging(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",
    "        \n",
    "        where_0 = np.argwhere(class_probs == 0)\n",
    "        for elem in where_0:\n",
    "            class_probs[elem[0], elem[1]] = 1/(2*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 - 1/(2*row_sums[elem[0], None])\n",
    "        \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",
    "rf_entropy_estimate_bagging(np.array(X).reshape(-1, 1), y, 500, .32)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hard moon case:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "import time\n",
    "import warnings\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn import cluster, datasets, mixture\n",
    "from sklearn.neighbors import kneighbors_graph\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from itertools import cycle, islice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sample_moons(n_samples):\n",
    "    noisy_moons = datasets.make_moons(n_samples=n_samples, noise=.05)\n",
    "    return noisy_moons"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(0)\n",
    "X, y = sample_moons(5000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-23-3fe7e151a900>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mrf_entropy_estimate_bagging\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m<ipython-input-11-5d6bdf10639e>\u001b[0m in \u001b[0;36mrf_entropy_estimate_bagging\u001b[0;34m(X, y, n_estimators, max_samples, bootstrap, depth, min_samples_leaf, max_features)\u001b[0m\n\u001b[1;32m     24\u001b[0m         \u001b[0mposterior_class_counts\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mzeros\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnode_counts\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmodel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_classes_\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     25\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mprob_index\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mprob_indices\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 26\u001b[0;31m             \u001b[0mposterior_class_counts\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mtree\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mapply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mprob_index\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitem\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mprob_index\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     27\u001b[0m         \u001b[0mrow_sums\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mposterior_class_counts\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maxis\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     28\u001b[0m         \u001b[0mrow_sums\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mrow_sums\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.7/site-packages/sklearn/tree/tree.py\u001b[0m in \u001b[0;36mapply\u001b[0;34m(self, X, check_input)\u001b[0m\n\u001b[1;32m    463\u001b[0m         \"\"\"\n\u001b[1;32m    464\u001b[0m         \u001b[0mcheck_is_fitted\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'tree_'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 465\u001b[0;31m         \u001b[0mX\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_validate_X_predict\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcheck_input\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    466\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtree_\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mapply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    467\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.7/site-packages/sklearn/tree/tree.py\u001b[0m in \u001b[0;36m_validate_X_predict\u001b[0;34m(self, X, check_input)\u001b[0m\n\u001b[1;32m    371\u001b[0m         \u001b[0;34m\"\"\"Validate X whenever one tries to predict, apply, predict_proba\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    372\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mcheck_input\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 373\u001b[0;31m             \u001b[0mX\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcheck_array\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mDTYPE\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maccept_sparse\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"csr\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    374\u001b[0m             if issparse(X) and (X.indices.dtype != np.intc or\n\u001b[1;32m    375\u001b[0m                                 X.indptr.dtype != np.intc):\n",
      "\u001b[0;32m/usr/local/lib/python3.7/site-packages/sklearn/utils/validation.py\u001b[0m in \u001b[0;36mcheck_array\u001b[0;34m(array, accept_sparse, dtype, order, copy, force_all_finite, ensure_2d, allow_nd, ensure_min_samples, ensure_min_features, warn_on_dtype, estimator)\u001b[0m\n\u001b[1;32m    440\u001b[0m                     \u001b[0;34m\"your data has a single feature or array.reshape(1, -1) \"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    441\u001b[0m                     \"if it contains a single sample.\".format(array))\n\u001b[0;32m--> 442\u001b[0;31m             \u001b[0marray\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0matleast_2d\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    443\u001b[0m             \u001b[0;31m# To ensure that array flags are maintained\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    444\u001b[0m             \u001b[0marray\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdtype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0morder\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0morder\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcopy\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcopy\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "rf_entropy_estimate_bagging(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.99344393 0.00655607]\n",
      " [0.99078443 0.00921557]\n",
      " [0.99274003 0.00725997]\n",
      " ...\n",
      " [0.00474596 0.99525404]\n",
      " [0.00474596 0.99525404]\n",
      " [0.00542391 0.99457609]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.05714580736017023"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rf_entropy_estimate_bagging_revised(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6931471805599453"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_entropy(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.99527859 0.00472141]\n",
      " [0.99384261 0.00615739]\n",
      " [0.00478456 0.99521544]\n",
      " ...\n",
      " [0.99527859 0.00472141]\n",
      " [0.00478456 0.99521544]\n",
      " [0.99441305 0.00558695]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.642310685125639"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_mutual_information(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9266432661470078"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    ".6423/.693147"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def uncertainty_forests_estimate(X, y, n_estimators = 300, eval_split_size = .33,\n",
    "                                                  subsample_size = 0.5,\n",
    "                                                  depth = 30,\n",
    "                                                  min_samples_leaf = 1):\n",
    "    \"\"\"\n",
    "    Uncertainty forest algorithm for estimating conditional entropy.\n",
    "    The major steps are as follows:\n",
    "    1. Split samples into EVAL and TRAIN according to eval_split_size\n",
    "    2. Get subsample s from TRAIN samples according to subsample_size\n",
    "    3. Split s into two partitions: STRUCT and PROB\n",
    "    4. Train decision forest on STRUCT (this is just sklearn's fit function)\n",
    "    5. For each tree in forest:\n",
    "        i) Use PROB samples to compute probabilites in each leaf node\n",
    "        ii) Perform robust finite sampling on posteriors computed by PROB samples\n",
    "        iii) Use posterior to get probability that eval sample fell in leaf node\n",
    "        iv) Weight eval sample probabilities by number of samples in leaf node (get class counts)\n",
    "    6. Compute probabilities from class counts over entire forest\n",
    "    7. Use probabilities to compute conditional entropies\n",
    "    8. Return average conditional entropy over all eval samples\n",
    "\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    X: array-like\n",
    "        Training samples.\n",
    "\n",
    "    y: list\n",
    "        Class labels for training samples.\n",
    "    \n",
    "    n_estimators: int\n",
    "        Number of trees in forest.\n",
    "    \n",
    "    eval_split_size: float between 0 and 1\n",
    "        Percent of samples to include in evaluation partition.\n",
    "    \n",
    "    subsample_size: float between 0 and 1\n",
    "        Percent of non eval samples to use for a tree (subsample forms PROB and STRUCT samples).\n",
    "    \n",
    "    depth: int\n",
    "        Maximum depth in tree.\n",
    "\n",
    "    min_samples_leaf\n",
    "        Minimum number of samples in node to be considered leaf.\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    Conditional entropy estimate\n",
    "    \"\"\"\n",
    "\n",
    "    # split samples into eval and non eval\n",
    "    X_train, X_eval, y_train, _ = train_test_split(X, y, test_size=eval_split_size)\n",
    "\n",
    "    max_samples = int(X_train.shape[0]*subsample_size)\n",
    "    split_samples = max_samples // 2\n",
    "    model = BaggingClassifier(DecisionTreeClassifier(max_depth = depth, \n",
    "                              min_samples_leaf = min_samples_leaf,\n",
    "                              # set default maximum features to sqrt(total features)\n",
    "                              max_features = math.ceil(int(math.sqrt(X.shape[1])))),\n",
    "                              n_estimators = n_estimators,\n",
    "                              max_samples= split_samples,\n",
    "                              bootstrap = True)\n",
    "    \n",
    "    model.fit(X_train, y_train)\n",
    "    # Matrix used to compute final estimate\n",
    "    # Each entry is total number of PROB nodes of class y that fell into\n",
    "    # the same leaf nodes that a x_eval sample fell into.\n",
    "    class_counts = np.zeros((X_eval.shape[0], model.n_classes_))\n",
    "    for tree in model:\n",
    "\n",
    "        # get total unused samples indices\n",
    "        unsampled_indices = _generate_unsampled_indices(tree.random_state, len(X))\n",
    "        # shuffle unused sample indices\n",
    "        np.random.shuffle(unsampled_indices)\n",
    "        # take split_samples amount as PROB indices (honest sampling)\n",
    "        prob_indices = unsampled_indices[:split_samples]\n",
    "\n",
    "        # get all node counts in tree\n",
    "        node_counts = tree.tree_.n_node_samples\n",
    "\n",
    "        # use PROB samples to compute posterior for tree\n",
    "\n",
    "        # NOTE: this considers probabilities for all nodes in the tree.\n",
    "        # However, only leaf nodes will have relevant values\n",
    "        posterior_class_counts = np.zeros((len(node_counts), model.n_classes_))\n",
    "        # for each leaf, count number of samples with each class label that fell into leaf\n",
    "        # NOTE: unused leaf nodes will have probability 0 for every class\n",
    "\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",
    "        \n",
    "        # divide each leaf node by number of total samples that fell into leaf node\n",
    "        row_sums = posterior_class_counts.sum(axis=1)\n",
    "        # handle divide by 0 errors\n",
    "        row_sums[row_sums == 0] = 1\n",
    "        class_probs = (posterior_class_counts/row_sums[:, None])\n",
    "\n",
    "        # perform robust finite sampling\n",
    "        class_probs = robust_finite_sampling(class_probs, row_sums, model.n_classes_)\n",
    "\n",
    "        # Get probabilities from EVAL samples for final estimate\n",
    "        # Weigh the probailities by number of samples in leaf node\n",
    "        \n",
    "        # Get leaf nodes counts for each sample in EVAL\n",
    "        partition_counts = np.asarray([node_counts[x] for x in tree.apply(X_eval)])\n",
    "        # get probability for eval samples\n",
    "        eval_class_probs = [class_probs[x] for x in tree.apply(X_eval)]\n",
    "        eval_class_probs = np.array(eval_class_probs)\n",
    "        # Get total elements \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 += elems\n",
    "    # calculate p(y|X = x) for all x's\n",
    "    forest_probabilities = class_counts/class_counts.sum(axis = 1, keepdims = True)\n",
    "    entropies = -np.sum(np.log(forest_probabilities)*forest_probabilities, axis = 1)\n",
    "    # convert nan to 0\n",
    "    entropies = np.nan_to_num(entropies)\n",
    "    # return sample mean\n",
    "    return np.mean(entropies)\n",
    "\n",
    "\n",
    "def robust_finite_sampling(class_probs, row_sums, n_classes):\n",
    "    where_0 = np.argwhere(class_probs == 0)\n",
    "    for elem in where_0:\n",
    "        class_probs[elem[0], elem[1]] = 1/(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 - (n_classes - 1)/(n_classes*row_sums[elem[0], None])\n",
    "    return class_probs.tolist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.061387830325188124"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "uncertainty_forests_estimate(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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