Mutual Information.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "def get_multivariate_sample(n, d, mean):\n",
    "    x_sample = []\n",
    "    y_sample = []\n",
    "    means = np.zeros(d)\n",
    "    means[0] = mean\n",
    "    for i in range(n):\n",
    "        y = np.random.binomial(1, .5)\n",
    "        if (y == 0):\n",
    "            x = np.random.multivariate_normal(-means, np.identity(d))\n",
    "        else:\n",
    "            x = np.random.multivariate_normal(means, 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(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(1000, 2, 2)\n",
    "sample = list(zip(X, y))\n",
    "class_one, class_neg_one = split_by_class(sample)\n",
    "plt.scatter([x[0] for x in list(zip(*class_one))[0]], [x[1] for x in list(zip(*class_one))[0]], c = 'b')\n",
    "plt.scatter([x[0] for x in list(zip(*class_neg_one))[0]], [x[1] for x in list(zip(*class_neg_one))[0]], c = 'orange')\n",
    "plt.title(\"Distribution Plot with Mean = 2\")\n",
    "plt.show()\n",
    "\n",
    "X, y = get_multivariate_sample(1000, 2, 1)\n",
    "sample = list(zip(X, y))\n",
    "class_one, class_neg_one = split_by_class(sample)\n",
    "plt.scatter([x[0] for x in list(zip(*class_one))[0]], [x[1] for x in list(zip(*class_one))[0]], c = 'b')\n",
    "plt.scatter([x[0] for x in list(zip(*class_neg_one))[0]], [x[1] for x in list(zip(*class_neg_one))[0]], c = 'orange')\n",
    "plt.title(\"Distribution Plot with Mean = 1\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, y = get_multivariate_sample(5000, 1, 0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.3720380230136316"
      ]
     },
     "execution_count": 5,
     "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/(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",
    "\n",
    "rf_entropy_estimate_bagging(X, y, 200, .32)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.32151613807914453"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_mutual_information(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from tqdm import tqdm_notebook\n",
    "\n",
    "def mutual_information_v_mu(n, d):\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",
    "    mutual_infos = []\n",
    "    for mean in tqdm_notebook(means):\n",
    "        X, y = get_multivariate_sample(n, d, mean)\n",
    "        mutual_info = get_mutual_information(X, y)\n",
    "        mutual_infos.append(mutual_info)\n",
    "    return means, mutual_infos\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "bd200d69228b4ae2b982b96fba9eba3e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=51), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "means, mutual_infos = mutual_information_v_mu(20000, 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pickle\n",
    "#pickle.dump({\"means\": means, \"mutual_infos\": mutual_infos}, open(\"mutual_info_cef.p\", \"wb\"))\n",
    "data = pickle.load(open(\"cache/mutual_info_cef.p\", \"rb\"))\n",
    "mutual_infos_6 = data[\"mutual_infos\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import norm\n",
    "from scipy.stats import multivariate_normal\n",
    "import scipy.integrate as integrate\n",
    "import math\n",
    "from sklearn import mixture\n",
    "\n",
    "def estimate_p(y):\n",
    "    return y.count(1)/len(y)\n",
    "\n",
    "def estimate_x_params(X):\n",
    "    model = mixture.GaussianMixture(n_components = 2, covariance_type = \"full\")\n",
    "    model.fit(X)\n",
    "    return model.means_, model.covariances_\n",
    "    \n",
    "estimate_x_params(X)\n",
    "\n",
    "def normal_entropy_f(t, mean, var):\n",
    "    return -norm.pdf(t, mean, var)*np.log(norm.pdf(t, mean, var))\n",
    "\n",
    "def two_mixture_normals_entropy_f(t, mean_1, mean_2, var_1, var_2):\n",
    "    return -.5*norm.pdf(t, mean_1, var_1)*np.log(.5*norm.pdf(t, mean_1, var_1) + .5*norm.pdf(t, mean_2, var_2)) - .5*norm.pdf(t, mean_1, var_1)*np.log(.5*norm.pdf(t, mean_1, var_1) + .5*norm.pdf(t, mean_2, var_2))\n",
    "\n",
    "def normal_entropy(var):\n",
    "    return .5*np.log(2*math.pi*math.e*var)\n",
    "\n",
    "#NOTE: this doesn't work for mean = 0\n",
    "def plugin_estimate_cat_1D(X, y):\n",
    "    y_param = estimate_p(y)\n",
    "    x_params = estimate_x_params(X)\n",
    "    h_y = -y_param*np.log(y_param) - (1 - y_param)*np.log(1 - y_param)\n",
    "    #h_x_cond_y = integrate.quad(normal_entropy_f, -20, 20, args = (x_params[0][0], x_params[1][0].item()))[0]*.5 + \\\n",
    "    #integrate.quad(normal_entropy_f, -20, 20, args = (x_params[0][1], x_params[1][1].item()))[0]*.5\n",
    "    h_x_cond_y = normal_entropy(x_params[1][0])*.5 + normal_entropy(x_params[1][1])*.5\n",
    "    h_x = integrate.quad(two_mixture_normals_entropy_f, -20, 20, args = (x_params[0][0], x_params[0][1], x_params[1][0].item(), x_params[1][1].item()))[0]\n",
    "    cond_entropy =  h_y - h_x + h_x_cond_y\n",
    "    if cond_entropy < 0:\n",
    "        return np.array((0))\n",
    "    return cond_entropy\n",
    "\n",
    "def truth_1d(mean):\n",
    "    h_y = -.5*np.log(.5) - .5*np.log(.5)\n",
    "    h_x_cond_y = normal_entropy(1)*.5 + normal_entropy(1)*.5\n",
    "    h_x = integrate.quad(two_mixture_normals_entropy_f, -20, 20, args = (mean, -mean, 1, 1))[0]\n",
    "    cond_entropy =  h_y - h_x + h_x_cond_y\n",
    "    if cond_entropy < 0:\n",
    "        return np.array((0))\n",
    "    return cond_entropy\n",
    "\n",
    "\n",
    "def mutual_information_truth():\n",
    "    entropy = -.5*np.log(.5) - .5*np.log(.5)\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",
    "    truths = []\n",
    "    for elem in means:\n",
    "        truths.append(entropy - truth_1d(elem))\n",
    "    #return means, cef_all, plugin_all, truth\n",
    "    return truths"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "9fc4bcc83b0449aebdb7a455643f5f49",
       "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": [
    "truths = mutual_information_truth()\n",
    "from tqdm import tqdm_notebook\n",
    "import sys\n",
    "sys.path.insert(0, './code')\n",
    "import entropy_estimators as ee\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",
    "kraskov = []\n",
    "for mean in tqdm_notebook(means):\n",
    "    X, y = get_multivariate_sample(10000, 6, mean)\n",
    "    mutual_info = ee.mi(X, np.array(y).reshape(-1, 1))\n",
    "    kraskov.append(mutual_info)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e8166cafafa74ba0a490fea0259a3ad7",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=51), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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-27-bc6b9ddb0468>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     13\u001b[0m         \u001b[0mmutual_infos\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmixed\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mMixed_KSG\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[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\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[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     14\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mmeans\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmutual_infos\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 15\u001b[0;31m \u001b[0mmeans\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmutual_infos_ksg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmutual_information_v_mu_ksg\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m10000\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m6\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m<ipython-input-27-bc6b9ddb0468>\u001b[0m in \u001b[0;36mmutual_information_v_mu_ksg\u001b[0;34m(n, d)\u001b[0m\n\u001b[1;32m     11\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0mmean\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mtqdm_notebook\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmeans\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     12\u001b[0m         \u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_multivariate_sample\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0md\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmean\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 13\u001b[0;31m         \u001b[0mmutual_infos\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmixed\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mMixed_KSG\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[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\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[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     14\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mmeans\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmutual_infos\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     15\u001b[0m \u001b[0mmeans\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmutual_infos_ksg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmutual_information_v_mu_ksg\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m10000\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m6\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/neurodata/rf-independence/code/mixed.py\u001b[0m in \u001b[0;36mMixed_KSG\u001b[0;34m(x, y, k)\u001b[0m\n\u001b[1;32m     52\u001b[0m                 x[i], knn_dis[i]-1e-15, p=float('inf')))\n\u001b[1;32m     53\u001b[0m             ny = len(tree_y.query_ball_point(\n\u001b[0;32m---> 54\u001b[0;31m                 y[i], knn_dis[i]-1e-15, p=float('inf')))\n\u001b[0m\u001b[1;32m     55\u001b[0m         \u001b[0mans\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mdigamma\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkp\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mN\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mdigamma\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnx\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mdigamma\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mny\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mN\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     56\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mans\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "import sys\n",
    "sys.path.insert(0, './code')\n",
    "import mixed\n",
    "from tqdm import tqdm_notebook\n",
    "\n",
    "def mutual_information_v_mu_ksg(n, d):\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",
    "    mutual_infos = []\n",
    "    for mean in tqdm_notebook(means):\n",
    "        X, y = get_multivariate_sample(n, d, mean)\n",
    "        mutual_infos.append(mixed.Mixed_KSG(X, y.reshape(-1, 1)))\n",
    "    return means, mutual_infos\n",
    "means, mutual_infos_ksg = mutual_information_v_mu_ksg(10000, 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.67582312158065, 0.6753830158417373, 0.6755212026241914, 0.6750815624877556, 0.6749790736262449, 0.6751019177135343, 0.6759773085092778, 0.6756110521843239, 0.6742514580982617, 0.6742609672771221, 0.673748255226488, 0.6708320704533255, 0.6654446733984649, 0.6563969834652492, 0.643982903574075, 0.6234303254544172, 0.594697612289535, 0.5526708981152124, 0.48969078669683946, 0.41719426588941133, 0.3349702769400371, 0.25007627091888623, 0.15926703236216427, 0.07746077340630052, 0.02410375261845576, 0.003870378864389339, 0.025269524098349122, 0.07709240661285525, 0.15940885341503877, 0.24480076843566242, 0.33731408502948135, 0.4234748204832131, 0.49488423566295786, 0.547178589833303, 0.5935982442641261, 0.6252838607904839, 0.6447565350482498, 0.6583137568724401, 0.6674333471070255, 0.6719910946494987, 0.6744077816351639, 0.6742782001608295, 0.6757053113725628, 0.6763441299468579, 0.6757549093569294, 0.6747385558663067, 0.6740561219889551, 0.6749668925100226, 0.6748135291779361, 0.676954672535523, 0.6751728545951546]\n"
     ]
    }
   ],
   "source": [
    "print(mutual_infos_ksg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "ksg = [0.67582312158065, 0.6753830158417373, 0.6755212026241914, 0.6750815624877556, 0.6749790736262449, 0.6751019177135343, 0.6759773085092778, 0.6756110521843239, 0.6742514580982617, 0.6742609672771221, 0.673748255226488, 0.6708320704533255, 0.6654446733984649, 0.6563969834652492, 0.643982903574075, 0.6234303254544172, 0.594697612289535, 0.5526708981152124, 0.48969078669683946, 0.41719426588941133, 0.3349702769400371, 0.25007627091888623, 0.15926703236216427, 0.07746077340630052, 0.02410375261845576, 0.003870378864389339, 0.025269524098349122, 0.07709240661285525, 0.15940885341503877, 0.24480076843566242, 0.33731408502948135, 0.4234748204832131, 0.49488423566295786, 0.547178589833303, 0.5935982442641261, 0.6252838607904839, 0.6447565350482498, 0.6583137568724401, 0.6674333471070255, 0.6719910946494987, 0.6744077816351639, 0.6742782001608295, 0.6757053113725628, 0.6763441299468579, 0.6757549093569294, 0.6747385558663067, 0.6740561219889551, 0.6749668925100226, 0.6748135291779361, 0.676954672535523, 0.6751728545951546]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "entropy = -.5*np.log(.5) - .5*np.log(.5)\n",
    "ksg = ksg/entropy\n",
    "sns.set(font_scale = 2)\n",
    "sns.set_style(\"ticks\")\n",
    "plt.rcParams[\"font.family\"] = \"sans-serif\"\n",
    "plt.rcParams['figure.figsize'] = [15, 10]\n",
    "\n",
    "line_cef, = plt.plot(means, np.array(mutual_infos_6)/entropy, label = \"CEF\", linewidth = 2, color = \"#F41711\")\n",
    "line_truth, = plt.plot(means, np.array(truths)/entropy, label = \"Truth\", linewidth = 2, color = \"black\")\n",
    "line_kraskov, = plt.plot(means, kraskov, label = \"Kraskov\", linewidth = 2, color = \"#35978f\")\n",
    "line_ksg, = plt.plot(means, ksg, label = \"Mixed KSG\", linewidth = 2, color = \"#fdae61\")\n",
    "\n",
    "\n",
    "\n",
    "plt.xlabel(u'\\u03bc')\n",
    "plt.ylabel(\"Mutual Information\")\n",
    "#plt.ylim(ymin = 0)\n",
    "#plt.ylim(ymax = .9)\n",
    "plt.legend(handles=[line_cef, line_ksg, line_kraskov, line_truth])\n",
    "plt.tight_layout()\n",
    "plt.savefig(\"mi_normalized.png\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "mutual_infos_40 = [1.0000214609365372,\n",
    " 0.9999986733222244,\n",
    " 1.00001580554283,\n",
    " 1.0000173059651303,\n",
    " 0.9999967977546902,\n",
    " 0.9995252030727215,\n",
    " 0.9988067607395834,\n",
    " 0.9989307394187819,\n",
    " 0.9944666797690189,\n",
    " 0.9908065503408636,\n",
    " 0.9869156471862937,\n",
    " 0.9706095230934864,\n",
    " 0.9496053896874486,\n",
    " 0.9073124129020584,\n",
    " 0.8524048887242799,\n",
    " 0.768586624680168,\n",
    " 0.6634438524987303,\n",
    " 0.528799412786114,\n",
    " 0.35732001634342225,\n",
    " 0.15226916766270904,\n",
    " 0.05812406897661049,\n",
    " 0.,\n",
    " 0.,\n",
    " 0.,\n",
    " 0.,\n",
    " 0.,\n",
    " 0.,\n",
    " 0.,\n",
    " 0.,\n",
    " 0.,\n",
    " 0.04548867792939859,\n",
    " 0.14772307178171218,\n",
    " 0.33455158920307326,\n",
    " 0.5340914617796102,\n",
    " 0.6586444799900022,\n",
    " 0.7745653613346377,\n",
    " 0.8607384462347483,\n",
    " 0.9150521638484008,\n",
    " 0.9492816518052365,\n",
    " 0.9677988217723907,\n",
    " 0.9853615950316339,\n",
    " 0.9915960998552293,\n",
    " 0.9956172301670136,\n",
    " 0.9986236217426949,\n",
    " 0.9991428336189472,\n",
    " 0.9996984417048509,\n",
    " 0.9999397430642887,\n",
    " 1.0000272317470973,\n",
    " 0.9999339158596285,\n",
    " 1.000010099602548,\n",
    " 0.9999965669074697]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ca1a4c7f5a394a8d99efb8f69cf781de",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=51), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "means, mutual_infos_ksg_40 = mutual_information_v_mu_ksg(20000, 40)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05]\n"
     ]
    }
   ],
   "source": [
    "print(mutual_infos_ksg_40)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "mutual_infos_ksg_40 = [2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05, 2.5000208333724202e-05]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "ename": "KeyError",
     "evalue": "'truths'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-2-3ea2a507c6b8>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mmutual_infos\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"mutual_infos\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0mmeans\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"means\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m \u001b[0mtruths\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"truths\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mKeyError\u001b[0m: 'truths'"
     ]
    }
   ],
   "source": [
    "import pickle\n",
    "#means, mutual_infos = mutual_information_v_mu(20000, 40)\n",
    "#pickle.dump({\"means\": means, \"mutual_infos\": mutual_infos, \"truth\": truths}, open(\"mutual_info_cef_40d.p\", \"wb\"))\n",
    "data = pickle.load(open(\"cache/mutual_info_cef_40d.p\", \"rb\"))\n",
    "mutual_infos = data[\"mutual_infos\"]\n",
    "means = data[\"means\"]\n",
    "truths = data[\"truths\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'np' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-3-c9fffb79cdbd>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpyplot\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mget_ipython\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun_line_magic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'matplotlib'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'inline'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0mentropy\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m.5\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m.5\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m.5\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m.5\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      5\u001b[0m \u001b[0msns\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfont_scale\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0msns\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_style\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"ticks\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'np' is not defined"
     ]
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "entropy = -.5*np.log(.5) - .5*np.log(.5)\n",
    "sns.set(font_scale = 2)\n",
    "sns.set_style(\"ticks\")\n",
    "plt.rcParams[\"font.family\"] = \"sans-serif\"\n",
    "plt.rcParams['figure.figsize'] = [15, 10]\n",
    "\n",
    "line_cef, = plt.plot(means, np.array(mutual_infos)/entropy, label = \"CEF\", linewidth = 2, color = \"#F41711\")\n",
    "line_truth, = plt.plot(means, np.array(truths)/entropy, label = \"Truth\", linewidth = 2, color = \"black\")\n",
    "line_kraskov, = plt.plot(means, mutual_infos_40, label = \"Kraskov\", linewidth = 2, color = \"#35978f\")\n",
    "line_ksg, = plt.plot(means, mutual_infos_ksg_40/entropy, label = \"Mixed KSG\", linewidth = 2, color = \"#fdae61\")\n",
    "\n",
    "\n",
    "plt.xlabel(u'\\u03bc')\n",
    "plt.ylabel(\"Mutual Information\")\n",
    "#plt.ylim(ymin = 0)\n",
    "#plt.ylim(ymax = .9)\n",
    "plt.legend(handles=[line_cef, line_ksg, line_kraskov, line_truth])\n",
    "plt.tight_layout()\n",
    "plt.savefig(\"mi_normalized_40d.png\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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