Mutual Information Settings 2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
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     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1979\n",
      "21\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
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     "metadata": {},
     "output_type": "display_data"
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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "\n",
    "def get_multivariate_sample(n, d, mean, p = .5, spherical = True, truncated = False):\n",
    "    cov_1 = np.identity(d)\n",
    "    cov_2 = np.identity(d)\n",
    "    if not spherical:\n",
    "        diag = np.ones(d)\n",
    "        diag[0] = 3\n",
    "        cov_2 = np.diag(diag)\n",
    "    x_sample = []\n",
    "    y_sample = []\n",
    "    means = np.zeros(d)\n",
    "    means[0] = mean\n",
    "        \n",
    "    while len(y_sample) < n:\n",
    "        y = np.random.binomial(1, p)\n",
    "        if (y == 0):\n",
    "            x = np.random.multivariate_normal(-means, cov_1)                \n",
    "        else:\n",
    "            x = np.random.multivariate_normal(means, cov_2)\n",
    "        if truncated and y == 0 and x[0] > 0:\n",
    "            continue\n",
    "        elif truncated and y == 1 and x[0] < 0:\n",
    "            continue\n",
    "        else:\n",
    "            x_sample.append(x.tolist())\n",
    "            y_sample.append(y)\n",
    "    return np.array(x_sample), np.array(y_sample)\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_multivariate_sample(10000, 2, 2)\n",
    "sample = list(zip(X, y))\n",
    "class_one, class_neg_one = split_by_class(sample)\n",
    "sns.kdeplot([x[0] for x in list(zip(*class_one))[0]], [x[1] for x in list(zip(*class_one))[0]], color = \"blue\")\n",
    "sns.kdeplot([x[0] for x in list(zip(*class_neg_one))[0]], [x[1] for x in list(zip(*class_neg_one))[0]], color = \"orange\")\n",
    "plt.title(\"Distribution Plot with Mean = 2, p = .5\")\n",
    "plt.show()\n",
    "\n",
    "X, y = get_multivariate_sample(2000, 2, 1, .99)\n",
    "sample = list(zip(X, y))\n",
    "class_one, class_neg_one = split_by_class(sample)\n",
    "print(len(class_one))\n",
    "print(len(class_neg_one))\n",
    "sns.kdeplot([x[0] for x in list(zip(*class_one))[0]], [x[1] for x in list(zip(*class_one))[0]], color = \"blue\")\n",
    "sns.kdeplot([x[0] for x in list(zip(*class_neg_one))[0]], [x[1] for x in list(zip(*class_neg_one))[0]], color = \"orange\")\n",
    "plt.title(\"Distribution Plot with Mean = 0, p = .999\")\n",
    "plt.show()\n",
    "\n",
    "X, y = get_multivariate_sample(10000, 2, 2, .5, False)\n",
    "sample = list(zip(X, y))\n",
    "class_one, class_neg_one = split_by_class(sample)\n",
    "sns.kdeplot([x[0] for x in list(zip(*class_one))[0]], [x[1] for x in list(zip(*class_one))[0]], color = \"blue\")\n",
    "sns.kdeplot([x[0] for x in list(zip(*class_neg_one))[0]], [x[1] for x in list(zip(*class_neg_one))[0]], color = \"orange\")\n",
    "plt.title(\"Distribution Plot with Mean = 1, p = .5, \")\n",
    "plt.show()\n",
    "\n",
    "X, y = get_multivariate_sample(5000, 2, 0, .5, True, True)\n",
    "sample = list(zip(X, y))\n",
    "class_one, class_neg_one = split_by_class(sample)\n",
    "sns.kdeplot([x[0] for x in list(zip(*class_one))[0]], [x[1] for x in list(zip(*class_one))[0]], color = \"blue\")\n",
    "sns.kdeplot([x[0] for x in list(zip(*class_neg_one))[0]], [x[1] for x in list(zip(*class_neg_one))[0]], color = \"orange\")\n",
    "plt.title(\"Distribution Plot with Mean = 1, p = .5, \")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def three_class_multivariate(n, d, mean):\n",
    "    mean_1 = np.zeros(d)\n",
    "    mean_1[0] = mean\n",
    "    mean_2 = np.zeros(d)\n",
    "    mean_2[0] = -mean\n",
    "    mean_3 = np.zeros(d)\n",
    "    mean_3[1] = mean\n",
    "    x_sample = []\n",
    "    y_sample = []\n",
    "    for i in range(n):\n",
    "        y = np.random.multinomial(1, [1/3.]*3).flatten()\n",
    "        y = np.argwhere(y == 1).item()\n",
    "        if y == 0:\n",
    "            x = np.random.multivariate_normal(mean_1, np.identity(d))\n",
    "        elif y == 1:\n",
    "            x = np.random.multivariate_normal(mean_2, np.identity(d))\n",
    "        else:\n",
    "            x = np.random.multivariate_normal(mean_3, np.identity(d))\n",
    "        x_sample.append(x.tolist())\n",
    "        y_sample.append(y)\n",
    "    return np.array(x_sample), np.array(y_sample)\n",
    "\n",
    "def split_by_class_3(sample):\n",
    "    y_one = [pair for pair in sample if pair[1] == 0]\n",
    "    y_two = [pair for pair in sample if pair[1] == 1]\n",
    "    y_three = [pair for pair in sample if pair[1] == 2]\n",
    "    return y_one, y_two, y_three\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
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     "name": "stdout",
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      "0\n",
      "0\n",
      "0\n",
      "1\n",
      "1\n",
      "0\n",
      "0\n",
      "2\n",
      "1\n",
      "1\n",
      "1\n",
      "0\n",
      "1\n",
      "0\n",
      "2\n",
      "2\n",
      "1\n",
      "2\n",
      "2\n",
      "2\n",
      "1\n",
      "0\n",
      "0\n",
      "1\n",
      "2\n",
      "0\n",
      "0\n",
      "0\n",
      "0\n",
      "0\n",
      "2\n",
      "2\n",
      "1\n",
      "2\n",
      "2\n",
      "2\n",
      "0\n",
      "0\n",
      "1\n",
      "0\n",
      "1\n",
      "0\n",
      "2\n",
      "1\n",
      "2\n",
      "0\n",
      "0\n",
      "2\n",
      "2\n",
      "0\n",
      "0\n",
      "2\n",
      "2\n",
      "1\n",
      "1\n",
      "2\n",
      "0\n",
      "0\n",
      "0\n",
      "2\n",
      "1\n",
      "1\n",
      "1\n",
      "0\n",
      "1\n",
      "1\n",
      "2\n",
      "2\n",
      "2\n",
      "0\n",
      "0\n",
      "2\n",
      "1\n",
      "1\n",
      "1\n",
      "2\n",
      "0\n",
      "1\n",
      "0\n",
      "0\n",
      "0\n",
      "1\n",
      "0\n",
      "2\n",
      "0\n",
      "0\n",
      "2\n",
      "1\n",
      "0\n",
      "0\n",
      "0\n",
      "0\n",
      "2\n",
      "2\n",
      "2\n",
      "1\n",
      "1\n",
      "0\n",
      "1\n",
      "0\n",
      "1\n",
      "0\n",
      "0\n",
      "2\n",
      "0\n",
      "1\n",
      "0\n",
      "1\n",
      "1\n",
      "1\n",
      "1\n",
      "1\n",
      "1\n",
      "2\n",
      "1\n",
      "1\n",
      "[0 0 1 ... 2 1 1]\n"
     ]
    }
   ],
   "source": [
    "X, y = three_class_multivariate(10000, 2, 2)\n",
    "print(y)\n",
    "sample = list(zip(X, y))\n",
    "class_one, class_two, class_three = split_by_class_3(sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11b0fc278>"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "sns.kdeplot([x[0] for x in list(zip(*class_one))[0]], [x[1] for x in list(zip(*class_one))[0]], color = \"blue\")\n",
    "sns.kdeplot([x[0] for x in list(zip(*class_two))[0]], [x[1] for x in list(zip(*class_two))[0]])\n",
    "sns.kdeplot([x[0] for x in list(zip(*class_three))[0]], [x[1] for x in list(zip(*class_three))[0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.7/site-packages/sklearn/ensemble/weight_boosting.py:29: DeprecationWarning: numpy.core.umath_tests is an internal NumPy module and should not be imported. It will be removed in a future NumPy release.\n",
      "  from numpy.core.umath_tests import inner1d\n"
     ]
    }
   ],
   "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/(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[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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "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 = rf_entropy_estimate_bagging(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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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_mu(n, d, spherical = True, truncated = False):\n",
    "    means = [i*.2 for i in range(0, 26)]\n",
    "    #means.reverse()\n",
    "    #means.extend([i*.2 for i in range(1, 26)])\n",
    "    cef = []\n",
    "    kraskov = []\n",
    "    mixed_ksg = []\n",
    "    for mean in tqdm_notebook(means):\n",
    "        X, y = get_multivariate_sample(n, d, mean, .5, spherical, truncated)\n",
    "        kraskov.append(ee.micd(X, y.reshape(-1, 1)))\n",
    "        cef.append(get_mutual_information(X, y))\n",
    "        mixed_ksg.append(mixed.Mixed_KSG(X, y.reshape(-1, 1)))\n",
    "    return means, cef, kraskov, mixed_ksg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "869a11331d81431aa42559859b7ac608",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=51), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "means, cef_ellipse, kraskov_ellipse, mixed_ellipse = mutual_information_v_mu(10000, 6, False, False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pickle\n",
    "pickle.dump({\"means\": means, \"cef_ellipse\": cef_ellipse, \"kraskov_ellipse\": kraskov_ellipse, \"mixed_ellipse\": mixed_ellipse}, open(\"mi_ellipse.p\", \"wb\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b7c0b03f91d845afaee3efd674ec4e95",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=51), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "means, cef_ellipse_40, kraskov_ellipse_40, mixed_ellipse_40 = mutual_information_v_mu(10000, 40, False, False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [],
   "source": [
    "pickle.dump({\"means\": means, \"cef_ellipse\": cef_ellipse_40, \"kraskov_ellipse\": kraskov_ellipse_40, \"mixed_ellipse\": mixed_ellipse_40}, open(\"mi_ellipse_40.p\", \"wb\"))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "1bf3307955f04b7bb3431463f556e2ac",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=26), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "means, cef_trunc, kraskov_trunc, mixed_trunc = mutual_information_v_mu(10000, 6, True, True)\n",
    "pickle.dump({\"means\": means, \"cef\": cef_trunc, \"kraskov\": kraskov_trunc, \"mixed\": mixed_trunc}, open(\"mi_trunc.p\", \"wb\"))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a4ecf3b00d1f4f0f850b5ac50d148ae1",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=26), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "means, cef_trunc_40, kraskov_trunc_40, mixed_trunc_40 = mutual_information_v_mu(10000, 40, True, True)\n",
    "pickle.dump({\"means\": means, \"cef\": cef_trunc_40, \"kraskov\": kraskov_trunc_40, \"mixed\": mixed_trunc_40}, open(\"mi_trunc_40.p\", \"wb\"))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5a86cd81b34e418dbda28dc833ae6fbb",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=26), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "019f622c9cd444ffba851c8c5a9b7924",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=26), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "import pickle\n",
    "def mutual_information_v_p(n, d):\n",
    "    probs = [i*.02 for i in range(0, 26)]\n",
    "    cef = []\n",
    "    kraskov = []\n",
    "    mixed_ksg = []\n",
    "    for p in tqdm_notebook(probs):\n",
    "        X, y = get_multivariate_sample(n, d, 1, p, spherical=True, truncated=False)\n",
    "        cef.append(get_mutual_information(X, y))\n",
    "        kraskov.append(ee.micd(X, y.reshape(-1, 1)))\n",
    "        mixed_ksg.append(mixed.Mixed_KSG(X, y.reshape(-1, 1)))\n",
    "    return probs, cef, kraskov, mixed_ksg\n",
    "\n",
    "probs, cef_p, kraskov_p, mixed_p = mutual_information_v_p(10000, 6)\n",
    "pickle.dump({\"probs\": probs, \"cef\": cef_p, \"kraskov\": kraskov_p, \"mixed\": mixed_p}, open(\"mi_prob.p\", \"wb\"))\n",
    "\n",
    "\n",
    "probs, cef_p_40, kraskov_p_40, mixed_p_40 = mutual_information_v_p(10000, 40)\n",
    "pickle.dump({\"probs\": probs, \"cef\": cef_p_40, \"kraskov\": kraskov_p_40, \"mixed\": mixed_p_40}, open(\"mi_prob_40.p\", \"wb\"))\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def mutual_information_v_mu_three_class(n, d):\n",
    "\n",
    "    means=[i*.2 for i in range(1, 26)]\n",
    "    cef = []\n",
    "    kraskov = []\n",
    "    mixed_ksg = []\n",
    "    for mean in tqdm_notebook(means):\n",
    "        X, y = three_class_multivariate(n, d, mean)\n",
    "        cef.append(get_mutual_information(X, y))\n",
    "        kraskov.append(ee.mi(X, y.reshape(-1, 1)))\n",
    "        mixed_ksg.append(mixed.Mixed_KSG(X, y.reshape(-1, 1)))\n",
    "    return means, cef, kraskov, mixed_ksg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "84a8a0e9963149d29fbc8d31fac20174",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=51), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "means, cef_three, kraskov_three, mixed_three = mutual_information_v_mu_three_class(10000, 6)\n",
    "pickle.dump({\"means\": means, \"cef\": cef_three, \"kraskov\": kraskov_three, \"mixed\": mixed_three}, open(\"mi_three_class_mi.p\", \"wb\"))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "cf204a19b6ee4bc890f300b55940a20a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=51), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "means, cef_three_40, kraskov_three_40, mixed_three_40 = mutual_information_v_mu_three_class(10000, 40)\n",
    "pickle.dump({\"means\": means, \"cef\": cef_three_40, \"kraskov\": kraskov_three_40, \"mixed\": mixed_three_40}, open(\"mi_three_class_40_mi.p\", \"wb\"))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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