MVA-2021 / computational_stats / hw2_sol.ipynb
hw2_sol.ipynb
Raw
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 270,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import torch\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.patches import Ellipse\n",
    "import matplotlib.transforms as transforms\n",
    "\n",
    "from scipy.stats import multivariate_normal\n",
    "\n",
    "import sklearn\n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn.preprocessing import LabelEncoder\n",
    "from sklearn.preprocessing import StandardScaler"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate a random variable $X$ having the discrete distribution on $X$ given by $p_i$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 271,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.array([1,2,3,4,5])\n",
    "p = np.array([0.1,0.2,0.1,0.3,0.3])\n",
    "p_cum = p.cumsum()\n",
    "\n",
    "def sample_x():\n",
    "    th = np.random.random()\n",
    "    for i,p in enumerate(p_cum):\n",
    "        if p>th:\n",
    "            break\n",
    "    return X[i] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 272,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.099807, 0.200622, 0.099791, 0.29945 , 0.30033 ])"
      ]
     },
     "execution_count": 272,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = 1000000\n",
    "X_sampled = [sample_x() for i in range(N)]\n",
    "np.histogram(X_sampled, bins=[1,2,3,4,5,6], density=True)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 2 - EM on Gaussian Mixture Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, generate the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 273,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def data_generator(cluster_nums, cluster_means, cluster_var):\n",
    "    data = []\n",
    "    for num, mu, var in zip(cluster_nums, cluster_means, cluster_var):\n",
    "        data += [np.random.multivariate_normal(mu, np.diag(var), num)]\n",
    "    data = np.vstack(data)\n",
    "    return data\n",
    "\n",
    "mus=[[0.5, 0.5],[6, 1.5],[1, 7]]\n",
    "vs = [[1, 3],[2, 2],[6, 2]]\n",
    "\n",
    "X = data_generator(cluster_nums=[40,60,80],\n",
    "                   cluster_means=mus,\n",
    "                   cluster_var=vs)\n",
    "\n",
    "def confidence_ellipse(mu, cov, ax, nstd=3.0, **kwargs):\n",
    "    def eigsorted(cov):\n",
    "        vals, vecs = np.linalg.eigh(cov)\n",
    "        order = vals.argsort()[::-1]\n",
    "        return vals[order], vecs[:,order]\n",
    "    if ax is None:\n",
    "        ax = plt.gca()\n",
    "    vals, vecs = eigsorted(cov)\n",
    "    theta = np.degrees(np.arctan2(*vecs[:,0][::-1]))\n",
    "    width, height = 2 * nstd * np.sqrt(vals)\n",
    "    ellip = Ellipse(xy=mu, width=width, height=height, angle=theta, facecolor=\"none\", **kwargs)\n",
    "    ax.add_artist(ellip)\n",
    "    return ellip\n",
    "\n",
    "ax = plt.axes()\n",
    "plt.scatter(X[:, 0], X[:, 1])\n",
    "\n",
    "for j in range(len(mus)):\n",
    "    confidence_ellipse(mus[j], np.diag(vs[j]), ax, edgecolor=\"r\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, we implement a gaussian mixture with EM optimization (using KMeans at initialization).\n",
    "The maximization step updates the parameters as following:\n",
    "$$ \\alpha_k =\\frac{1}{n} \\sum_{i=1}^n \\tau_{ik}$$\n",
    "$$ \\mu_k = \\frac{\\sum_{i=1}^n \\tau_{ik}x_i}{\\sum_{i=1}^n \\tau_{ik}}  $$ \n",
    "$$ \\Sigma_k = \\frac{\\sum_{i=1}^n \\tau_{ik}(x_i-\\mu_k)(x_i-\\mu_k)^T}{\\sum_{i=1}^n \\tau_{ik}}  $$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 274,
   "metadata": {},
   "outputs": [],
   "source": [
    "class GaussianMixture():\n",
    "\n",
    "    def __init__(self, n_components, n_iter):\n",
    "        \"\"\"Inits the GaussianMixture class by setting n_components and n_iter\"\"\"\n",
    "        self.n_components = n_components\n",
    "        self.n_iter = n_iter\n",
    "        \n",
    "    def fit_predict(self, X):\n",
    "        n = X.shape[0]\n",
    "        d = X.shape[1]\n",
    "        m = self.n_components\n",
    "        \n",
    "        #init with KMeans\n",
    "        kms = KMeans(n_clusters=m)\n",
    "        preds = kms.fit_predict(X)\n",
    "        \n",
    "        x_comp = [[] for _ in range(m)]\n",
    "        for i,pred in enumerate(preds):\n",
    "            x_comp[pred].append(X[i])\n",
    "        x_comp = [np.array(x) for x in x_comp]\n",
    "        \n",
    "        alpha = np.zeros(m)\n",
    "        mu = np.zeros((m, d))\n",
    "        sigma = np.zeros((m, d, d))\n",
    "        for i,x in enumerate(x_comp):\n",
    "            alpha[i] = x.shape[0] / n\n",
    "            mu[i] = np.mean(x)\n",
    "            sigma[i] = np.cov(x.T)\n",
    "        \n",
    "        # EM loop\n",
    "        for k in range(self.n_iter):\n",
    "\n",
    "            # Expectation\n",
    "            tau = np.zeros((m, n))\n",
    "            for j in range(m):\n",
    "                tau[j] = alpha[j] * multivariate_normal.pdf(X, mu[j], sigma[j])\n",
    "            print(np.sum(np.log(np.sum(tau, axis=0))))\n",
    "            tau /= tau.sum(axis=0)\n",
    "\n",
    "            # Maximization\n",
    "            a = np.sum(tau, axis=1)\n",
    "            alpha = a / np.sum(a)\n",
    "\n",
    "            mu = np.sum(tau[:,:,None]*X, axis=1) / a[:, None]\n",
    "\n",
    "            Xm = X - mu[:,None]\n",
    "            cov = Xm[:,:,:,None] * Xm[:,:,None,:]\n",
    "            sigma = np.sum(tau[:,:,None,None]*cov, axis=1) / a[:, None,None] + np.eye(d) * 1e-5\n",
    "            \n",
    "        self.alpha = alpha\n",
    "        self.mu = mu\n",
    "        self.sigma = sigma\n",
    "\n",
    "        return np.argmax(tau, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 275,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1181.299439000224\n",
      "-899.5267443856969\n",
      "-897.4591198070252\n",
      "-896.5364511128339\n",
      "-895.8997591264215\n",
      "-895.3411677144961\n",
      "-894.756064261031\n",
      "-894.0431439845474\n",
      "-893.045343754668\n",
      "-891.4488009012468\n",
      "-888.5468817347537\n",
      "-882.8186117183035\n",
      "-872.5582913934986\n",
      "-860.7569204535862\n",
      "-852.7599929175881\n",
      "-848.0514827286263\n",
      "-845.8214665510453\n",
      "-845.0282564507818\n",
      "-844.8098786642217\n",
      "-844.7601744018702\n",
      "-844.7495384325724\n",
      "-844.7472233700167\n",
      "-844.7466933272761\n",
      "-844.7465644704221\n",
      "-844.7465313710006\n",
      "-844.7465224885225\n",
      "-844.7465200268292\n",
      "-844.7465193281882\n",
      "-844.7465191259755\n",
      "-844.7465190662443\n",
      "-844.7465190481273\n",
      "-844.7465190424157\n",
      "-844.7465190405098\n",
      "-844.7465190398233\n",
      "-844.7465190395526\n",
      "-844.7465190394357\n",
      "-844.7465190393814\n",
      "-844.7465190393546\n",
      "-844.7465190393409\n",
      "-844.7465190393337\n",
      "-844.74651903933\n",
      "-844.746519039328\n",
      "-844.746519039327\n",
      "-844.7465190393264\n",
      "-844.7465190393261\n",
      "-844.7465190393258\n",
      "-844.7465190393257\n",
      "-844.7465190393257\n",
      "-844.7465190393257\n",
      "-844.7465190393256\n"
     ]
    }
   ],
   "source": [
    "gmm = GaussianMixture(n_components=3, n_iter=50)\n",
    "pred_gmm = gmm.fit_predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 276,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.21980044 0.31472435]\n",
      " [1.47255539 7.07331143]\n",
      " [6.22104491 1.09516433]]\n",
      "[[[ 0.82147098  0.08182729]\n",
      "  [ 0.08182729  3.4097929 ]]\n",
      "\n",
      " [[ 6.40287642  0.05263612]\n",
      "  [ 0.05263612  2.05576742]]\n",
      "\n",
      " [[ 2.07833038 -0.13730235]\n",
      "  [-0.13730235  1.08852956]]]\n"
     ]
    }
   ],
   "source": [
    "print(gmm.mu) # original [[0.5, 0.5], [6, 1.5], [1, 7]]\n",
    "print(gmm.sigma) # original [1, 3], [2, 2], [6, 2]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see, as expected, that the estimated means and variance are not far from original ones. *red* gives the expected ellipses, *green* the ground truth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 277,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = plt.axes()\n",
    "plt.scatter(X[:, 0], X[:, 1], c=pred_gmm)\n",
    "plt.suptitle('GMM clusters')\n",
    "\n",
    "for j in range(len(gmm.mu)):\n",
    "    confidence_ellipse(gmm.mu[j], gmm.sigma[j], ax, edgecolor=\"r\")\n",
    "for j in range(len(gmm.mu)):\n",
    "    confidence_ellipse(mus[j], np.diag(vs[j]), ax, edgecolor=\"g\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now try with real world data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 278,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13290  observations in the dataset\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>LocID</th>\n",
       "      <th>Location</th>\n",
       "      <th>VarID</th>\n",
       "      <th>Variant</th>\n",
       "      <th>Time</th>\n",
       "      <th>MidPeriod</th>\n",
       "      <th>TFR</th>\n",
       "      <th>NRR</th>\n",
       "      <th>CBR</th>\n",
       "      <th>Births</th>\n",
       "      <th>...</th>\n",
       "      <th>CDR</th>\n",
       "      <th>Deaths</th>\n",
       "      <th>DeathsMale</th>\n",
       "      <th>DeathsFemale</th>\n",
       "      <th>CNMR</th>\n",
       "      <th>NetMigrations</th>\n",
       "      <th>GrowthRate</th>\n",
       "      <th>NatIncr</th>\n",
       "      <th>SRB</th>\n",
       "      <th>MAC</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4</td>\n",
       "      <td>Afghanistan</td>\n",
       "      <td>2</td>\n",
       "      <td>Medium</td>\n",
       "      <td>1950-1955</td>\n",
       "      <td>1953</td>\n",
       "      <td>7.45</td>\n",
       "      <td>1.636</td>\n",
       "      <td>50.314</td>\n",
       "      <td>2015.476</td>\n",
       "      <td>...</td>\n",
       "      <td>36.862</td>\n",
       "      <td>1476.605</td>\n",
       "      <td>794.020</td>\n",
       "      <td>682.585</td>\n",
       "      <td>-0.499</td>\n",
       "      <td>-20.0</td>\n",
       "      <td>1.296</td>\n",
       "      <td>13.452</td>\n",
       "      <td>1.06</td>\n",
       "      <td>29.835</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4</td>\n",
       "      <td>Afghanistan</td>\n",
       "      <td>2</td>\n",
       "      <td>Medium</td>\n",
       "      <td>1955-1960</td>\n",
       "      <td>1958</td>\n",
       "      <td>7.45</td>\n",
       "      <td>1.765</td>\n",
       "      <td>50.998</td>\n",
       "      <td>2201.589</td>\n",
       "      <td>...</td>\n",
       "      <td>33.718</td>\n",
       "      <td>1455.605</td>\n",
       "      <td>783.110</td>\n",
       "      <td>672.495</td>\n",
       "      <td>-0.463</td>\n",
       "      <td>-20.0</td>\n",
       "      <td>1.683</td>\n",
       "      <td>17.280</td>\n",
       "      <td>1.06</td>\n",
       "      <td>29.835</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4</td>\n",
       "      <td>Afghanistan</td>\n",
       "      <td>2</td>\n",
       "      <td>Medium</td>\n",
       "      <td>1960-1965</td>\n",
       "      <td>1963</td>\n",
       "      <td>7.45</td>\n",
       "      <td>1.899</td>\n",
       "      <td>51.477</td>\n",
       "      <td>2439.130</td>\n",
       "      <td>...</td>\n",
       "      <td>30.808</td>\n",
       "      <td>1459.784</td>\n",
       "      <td>777.437</td>\n",
       "      <td>682.347</td>\n",
       "      <td>-0.422</td>\n",
       "      <td>-20.0</td>\n",
       "      <td>2.026</td>\n",
       "      <td>20.669</td>\n",
       "      <td>1.06</td>\n",
       "      <td>29.835</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>Afghanistan</td>\n",
       "      <td>2</td>\n",
       "      <td>Medium</td>\n",
       "      <td>1965-1970</td>\n",
       "      <td>1968</td>\n",
       "      <td>7.45</td>\n",
       "      <td>2.017</td>\n",
       "      <td>51.646</td>\n",
       "      <td>2728.221</td>\n",
       "      <td>...</td>\n",
       "      <td>28.223</td>\n",
       "      <td>1490.896</td>\n",
       "      <td>790.745</td>\n",
       "      <td>700.151</td>\n",
       "      <td>-0.379</td>\n",
       "      <td>-20.0</td>\n",
       "      <td>2.307</td>\n",
       "      <td>23.423</td>\n",
       "      <td>1.06</td>\n",
       "      <td>29.835</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>Afghanistan</td>\n",
       "      <td>2</td>\n",
       "      <td>Medium</td>\n",
       "      <td>1970-1975</td>\n",
       "      <td>1973</td>\n",
       "      <td>7.45</td>\n",
       "      <td>2.141</td>\n",
       "      <td>51.234</td>\n",
       "      <td>3056.451</td>\n",
       "      <td>...</td>\n",
       "      <td>25.495</td>\n",
       "      <td>1520.938</td>\n",
       "      <td>802.414</td>\n",
       "      <td>718.524</td>\n",
       "      <td>-0.335</td>\n",
       "      <td>-20.0</td>\n",
       "      <td>2.544</td>\n",
       "      <td>25.739</td>\n",
       "      <td>1.06</td>\n",
       "      <td>29.835</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 25 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   LocID     Location  VarID Variant       Time  MidPeriod   TFR    NRR  \\\n",
       "0      4  Afghanistan      2  Medium  1950-1955       1953  7.45  1.636   \n",
       "1      4  Afghanistan      2  Medium  1955-1960       1958  7.45  1.765   \n",
       "2      4  Afghanistan      2  Medium  1960-1965       1963  7.45  1.899   \n",
       "3      4  Afghanistan      2  Medium  1965-1970       1968  7.45  2.017   \n",
       "4      4  Afghanistan      2  Medium  1970-1975       1973  7.45  2.141   \n",
       "\n",
       "      CBR    Births  ...     CDR    Deaths  DeathsMale  DeathsFemale   CNMR  \\\n",
       "0  50.314  2015.476  ...  36.862  1476.605     794.020       682.585 -0.499   \n",
       "1  50.998  2201.589  ...  33.718  1455.605     783.110       672.495 -0.463   \n",
       "2  51.477  2439.130  ...  30.808  1459.784     777.437       682.347 -0.422   \n",
       "3  51.646  2728.221  ...  28.223  1490.896     790.745       700.151 -0.379   \n",
       "4  51.234  3056.451  ...  25.495  1520.938     802.414       718.524 -0.335   \n",
       "\n",
       "   NetMigrations  GrowthRate  NatIncr   SRB     MAC  \n",
       "0          -20.0       1.296   13.452  1.06  29.835  \n",
       "1          -20.0       1.683   17.280  1.06  29.835  \n",
       "2          -20.0       2.026   20.669  1.06  29.835  \n",
       "3          -20.0       2.307   23.423  1.06  29.835  \n",
       "4          -20.0       2.544   25.739  1.06  29.835  \n",
       "\n",
       "[5 rows x 25 columns]"
      ]
     },
     "execution_count": 278,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(\"data.csv\",header = 0)\n",
    "df = df.dropna()\n",
    "print(df.shape[0], \" observations in the dataset\")\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 279,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = df[\"CBR\"].values\n",
    "y = df[\"CDR\"].values\n",
    "\n",
    "plt.scatter(x,y)\n",
    "plt.xlabel(\"birth\")\n",
    "plt.ylabel(\"death\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We don't see any simple dependencies, but it seems that we could decompose the data into 2 or 3 cluster of gaussian distributions. The idea of using GMM seems coherent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[50.314 36.862]\n",
      " [50.998 33.718]\n",
      " [51.477 30.808]\n",
      " ...\n",
      " [12.867 10.631]\n",
      " [12.492 11.191]\n",
      " [12.194 11.611]]\n"
     ]
    }
   ],
   "source": [
    "X = np.stack([x,y]).T\n",
    "print(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 281,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-126216.44246993324\n",
      "-82335.99227441972\n",
      "-81079.65022228232\n",
      "-80670.6129930956\n",
      "-80457.74127045723\n",
      "-80307.75274999619\n",
      "-80195.41089904602\n",
      "-80107.84324378896\n",
      "-80036.78978155417\n",
      "-79978.46631326897\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm = GaussianMixture(n_components=2, n_iter=10)\n",
    "pred_gmm = gmm.fit_predict(X)\n",
    "\n",
    "ax = plt.axes()\n",
    "plt.scatter(X[:, 0], X[:, 1], c=pred_gmm)\n",
    "plt.suptitle('GMM clusters')\n",
    "for j in range(len(gmm.mu)):\n",
    "    confidence_ellipse(gmm.mu[j], gmm.sigma[j], ax, edgecolor=\"r\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 282,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-139855.50333900825\n",
      "-80579.80566209057\n",
      "-79967.45995166636\n",
      "-79694.38147732407\n",
      "-79516.20280164244\n",
      "-79319.22590057948\n",
      "-79065.80160431171\n",
      "-78760.76648942534\n",
      "-78442.59687900002\n",
      "-78144.96688720482\n",
      "-77878.82601374602\n",
      "-77657.93437283544\n",
      "-77495.20087236438\n",
      "-77381.48985697834\n",
      "-77296.84775110886\n",
      "-77227.43164899822\n",
      "-77166.92860799504\n",
      "-77112.6041534151\n",
      "-77063.08270461444\n",
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    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm = GaussianMixture(n_components=3, n_iter=20)\n",
    "pred_gmm = gmm.fit_predict(X)\n",
    "ax = plt.axes()\n",
    "plt.scatter(X[:, 0], X[:, 1], c=pred_gmm)\n",
    "plt.suptitle('GMM clusters')\n",
    "for j in range(len(gmm.mu)):\n",
    "    confidence_ellipse(gmm.mu[j], gmm.sigma[j], ax, edgecolor=\"r\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 3 - Importance Sampling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3A - Poor Importance Sampling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 283,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return 2*math.sin(math.pi/1.5*x) if x>=0 else 0\n",
    "\n",
    "def p(x):\n",
    "    return x**(1.65-1)*math.exp(-0.5*x**2) if x>=0 else 0\n",
    "\n",
    "def q(x, mu=0.8, v=1.5):\n",
    "    return 2/(2*math.pi*v)**0.5 *math.exp(-(mu-x)**2/(2*v))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We implement a simple importance scheme for the previous functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 284,
   "metadata": {},
   "outputs": [],
   "source": [
    "def expect_imp_sampling(N=100,mu=0.8):\n",
    "    X = []\n",
    "    while len(X) <N:\n",
    "        x = np.random.randn()\n",
    "        if x >= 0:\n",
    "            X.append(x)\n",
    "    X = np.array(X)\n",
    "    ws = np.array([ p(x)/q(x, mu=mu) for x in X])\n",
    "    ws = ws/ ws.sum()\n",
    "    expect_f = sum([ w*f(X[i]) for i,w in enumerate(ws) ]) \n",
    "    return expect_f, ws, X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now compare the estimate and the importance weight for several sample size, $N = 10, 100, 10^3, 10^4$\n",
    "for instance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 285,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.4646107582347525\n"
     ]
    },
    {
     "data": {
      "image/png": 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4I5X/ObA2/ZzdwMMUEsnfAddFxNgxnGY519vdxTVLzxmTENy3ZI1AUWEURN719PREf39/XX6XFySzyfD/F8szSTsjomd0uReqG4cXJLPJKte35ARheeflKMbhBcmsVsULiqHhEc9OttxyMhiHZx5brXxBYY3AyWAcnnlstfIFhTUCJ4NxeOax1coXFNYInAzG4ZnHVitfUFgj8GiiCfDMY6tF8f+ORxNZnjkZmNWBLygs79xMZGZmTgZmZuZkYGZmOBmYmRlOBmZmhpOBmZnhoaVmueRVTq3enAwq8JvRsuJl0y0LbiYqw0sOW5a8yqllwcmgDL8ZLUte5dSy4GRQht+MliWvcmpZcDIow29Gy5JXObUsOBmU4TejZcnLplsWPJqogpNnzzrWbzDn1HbWX7HYb0arG69yavXmZDDK6GF9AP/v8LsZRmR2Ig97tplQUzORpE5Jj0j6qaSXJH1E0umStknak77PSXUl6S5JeyW9IOmCkp+zOtXfI2l1rX9ULTySyPLMw55tptTaZ/DfgL+LiH8JfBh4CVgLPBERi4An0nOAy4FF6WsNcDeApNOB9cBFwIXA+mICyYJHElme+WLFZsqUk4Gk9wK/D9wLEBHvRMQwsALYlKptAnrT4xXA/VGwHeiUdBawDNgWEQcj4hCwDVg+1bhq5ZFElme+WLGZUsudwW8DB4D/JWlA0jcknQZ8ICLeAEjf35/qdwGvlbx+MJVVKh9D0hpJ/ZL6Dxw4UEPolXkkkeWZL1ZsptSSDGYDFwB3R0Q38BuONwmVozJlUaV8bGHExojoiYieuXPnTjbeCfGwPsszX6zYTKllNNEgMBgRO9LzRygkg19IOisi3kjNQPtL6s8vef084PVU/tFR5T+oIa6aeVif5VXx/6VHE9l0m3IyiIj/K+k1SedGxMvApcBP0tdqYEP6/mh6yVbg85IepNBZ/GZKGI8D/7Wk0/gyYN1U4zJrdr5YsZlQ6zyD/wRslnQS8ArwOQpNTw9LuhbYB3wy1X0M+DiwF3gr1SUiDkr6CvBsqndLRBysMS4zM5sERZRtns+9np6e6O/vzzoMM7OGImlnRPSMLvcM5BKe2WlmrcrJIPHuUmbWyrxqaeKZnWbWypwMEs/sNLNW5mSQeGanmbUyJ4PEMzvNrJU5GZQ4efbx0zHn1HYvQ2FmLcOjifCGNmZmvjPAI4nMzJwM8EgiMzMnAzySyMzMyQCPJDIzcwcyXiPezMx3BniBOjOzlr8z8AJ1Zma+M/CwUjMznAwYqjB8tFK5mVkzavlkYGZmTgZmZoaTgZmZ4WRAR3v5U1Cp3MysGbX8J95tKz805iTMSuVmZq2i5mQgqU3SgKTvpOcLJe2QtEfSQ5JOSuUnp+d70/EFJT9jXSp/WdKyWmOajN7uLu64+ny6OjsQ0NXZwR1Xn+85BmbWUqZj0tkXgJeA96bnXwXujIgHJX0duBa4O30/FBG/I2lVqne1pPOAVcBi4Gzg7yX9bkQcHf2LZkpvd5c//M0mwbP2m09NdwaS5gGfAL6Rngu4BHgkVdkE9KbHK9Jz0vFLU/0VwIMR8XZEvArsBS6sJS4zmznFWftDwyMEx2ft9w0MZR2a1aDWZqKvAf8ZKG4LdgYwHBFH0vNBoHi50AW8BpCOv5nqHysv85oTSFojqV9S/4EDB2oM3cymwrP2m9OUk4GkPwT2R8TO0uIyVWOcY9Vec2JhxMaI6ImInrlz504qXjObHt4MqjnV0mdwMXClpI8Dp1DoM/ga0Clpdrr6nwe8nuoPAvOBQUmzgfcBB0vKi0pfY2Y5c3ZnR9nlWrwZVGOb8p1BRKyLiHkRsYBCB/CTEXEN8BRwVaq2Gng0Pd6anpOOPxkRkcpXpdFGC4FFwI+mGpeZzSxvBtWcZmIJ6xuBByXdCgwA96bye4G/kbSXwh3BKoCI2C3pYeAnwBHgunqOJDKzyfFmUM1JhYvzxtPT0xP9/f1Zh2Fm1lAk7YyIntHlLT8D2czMnAzMzAwnAzMzw8nAzMxwMjAzM5wMzMwMJwMzM8PJwMzMcDIwMzNmZjkKM7Mp8aY52XEyMLNcKG6aU9wrobhpDuCEUAduJjKzXPCmOdlyMjCzXPCmOdlq2WYit02a5Ys3zclWS94ZeENvs/zxpjnZaslk4LZJs/zp7e7itpVL6OrsQEBXZwe3rVziO/Y6aclmIrdNmuVTb3eXP/wz0pJ3BpXaIN02aWatqiWTgdsmzcxO1JLJAOCU9uN/emdHu9smzayltVyfwehZjgBvH3k3w4jMzLLXcncGHklkZjbWlJOBpPmSnpL0kqTdkr6Qyk+XtE3SnvR9TiqXpLsk7ZX0gqQLSn7W6lR/j6TVtf9ZlXkkkZnZWLXcGRwB/iIi/hWwFLhO0nnAWuCJiFgEPJGeA1wOLEpfa4C7oZA8gPXARcCFwPpiApkJHklkZjbWlJNBRLwRET9Oj38NvAR0ASuATanaJqA3PV4B3B8F24FOSWcBy4BtEXEwIg4B24DlU41rPB5JZGY21rR0IEtaAHQDO4APRMQbUEgYkt6fqnUBr5W8bDCVVSqfEcURQ16XyMzsuJqTgaT3AN8Cro+IX0mqWLVMWVQpL/e71lBoYuKcc86ZfLCJZzmamZ2optFEktopJILNEbElFf8iNf+Qvu9P5YPA/JKXzwNer1I+RkRsjIieiOiZO3duLaGbmVmJWkYTCbgXeCki7ig5tBUojghaDTxaUv6ZNKpoKfBmak56HLhM0pzUcXxZKjMzszqppZnoYuCPgF2SnktlXwQ2AA9LuhbYB3wyHXsM+DiwF3gL+BxARByU9BXg2VTvlog4WENcVXkfAzOzsRRRtnk+93p6eqK/v39Sryk3+7ijvc1LUZhZy5C0MyJ6Rpe31Axkzz42MyuvpZKBZx+bmZXXUsnAs4/NzMprqWTg2cdmZuW11BLWnn1sZlZeSyUD8OxjM7NyWqqZyMzMynMyMDMzJwMzM3MyMDMzWrAD2cysEc30umpOBmZmOTd6XbWh4RHWbdkFMG0Jwc1EZmY5V4911VruzsBLWJtZo6nHumotdWdQvNUaGh4hOH6r1TcwlHVoZmYV1WNdtZZKBl7C2swaUT3WVWupZiIvYW1mjage66q1VDI4u7ODoTIf/F7C2szybqbXVWupZiIvYW1mVl5L3Rl4CWszs/JaKhmAl7A2MyunpZqJzMysPCcDMzNzMjAzMycDMzPDycDMzABFRNYxTImkA8DPp/jyM4FfTmM4MyHvMeY9Psh/jHmPD/IfY97jg/zF+M8jYu7owoZNBrWQ1B8RPVnHUU3eY8x7fJD/GPMeH+Q/xrzHB40RI7iZyMzMcDIwMzNaNxlszDqACch7jHmPD/IfY97jg/zHmPf4oDFibM0+AzMzO1Gr3hmYmVkJJwMzM2vuZCBpuaSXJe2VtLbM8ZMlPZSO75C0IIcxflbSAUnPpa9/X+f47pO0X9KLFY5L0l0p/hckXZCz+D4q6c2S8/df6hzffElPSXpJ0m5JXyhTJ7NzOMH4sj6Hp0j6kaTnU4w3l6mT2Xt5gvFl+j6ekIhoyi+gDfgZ8NvAScDzwHmj6vwJ8PX0eBXwUA5j/CzwPzI8j78PXAC8WOH4x4HvAQKWAjtyFt9Hge9keP7OAi5Ij38L+Icy/8aZncMJxpf1ORTwnvS4HdgBLB1VJ7P38gTjy/R9PJGvZr4zuBDYGxGvRMQ7wIPAilF1VgCb0uNHgEslKWcxZioifggcrFJlBXB/FGwHOiWdVZ/oJhRfpiLijYj4cXr8a+AlYPSGGpmdwwnGl6l0Xv4pPW1PX6NHvmT2Xp5gfLnXzMmgC3it5PkgY/+TH6sTEUeAN4Ez6hLdqN+flIsR4N+k5oNHJM2vT2gTNtG/IUsfSbfw35O0OKsgUtNFN4Urx1K5OIdV4oOMz6GkNknPAfuBbRFR8Rxm8V6eQHyQ7/dxUyeDclcFo7P1ROrMpIn8/m8DCyLiQ8Dfc/zqJy+yPofj+TGFtVg+DPx3oC+LICS9B/gWcH1E/Gr04TIvqes5HCe+zM9hRByNiPOBecCFkj44qkqm53AC8eX9fdzUyWAQKM2+84DXK9WRNBt4H/Vtchg3xoj4x4h4Oz29B/i9OsU2URM5z5mJiF8Vb+Ej4jGgXdKZ9YxBUjuFD9rNEbGlTJVMz+F48eXhHJbEMgz8AFg+6lDW72WgcnwN8D5u6mTwLLBI0kJJJ1HoVNo6qs5WYHV6fBXwZKTenrzEOKrt+EoKbbp5shX4TBoRsxR4MyLeyDqoIkn/rNh2LOlCCv/n/7GOv1/AvcBLEXFHhWqZncOJxJeDczhXUmd63AH8AfDTUdUyey9PJL4GeB8zO+sAZkpEHJH0eeBxCqN27ouI3ZJuAfojYiuFN8HfSNpL4SpiVQ5j/FNJVwJHUoyfrWeMkh6gMJrkTEmDwHoKHWRExNeBxyiMhtkLvAV8LmfxXQX8saQjwAiwqs4J/2Lgj4BdqU0Z4IvAOSUxZnkOJxJf1ufwLGCTpDYKiejhiPhOjt7LE4kv0/fxRHg5CjMza+pmIjMzmyAnAzMzczIwMzMnAzMzw8nAzMxwMjAzM5wMzMwM+P+yshPZ+mccwgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.1678778364534208\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.2023525084291773\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.196573040380347\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.188089626807562\n"
     ]
    }
   ],
   "source": [
    "for n in [10,100,1000,10000, 100000]:\n",
    "    res = expect_imp_sampling(N=n)\n",
    "    plt.scatter(res[2], N*res[1])\n",
    "    plt.show()\n",
    "    print(res[0] )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this first case, the importance weights seem to follow the same distribution as $p$, meaning that the importance scheme works well. The estimation converges towards 1.194."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 286,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3997223491775006\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.2856052472824049\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.114393640244589\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.1251685145656105\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.1295058701784766\n"
     ]
    }
   ],
   "source": [
    "for n in [10,100,1000,10000, 100000]:\n",
    "    res = expect_imp_sampling(N=n, mu=6.0)\n",
    "    plt.scatter(res[2], N*res[1])\n",
    "    plt.show()\n",
    "    print(res[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that for $\\mu = 6$, where the centers of mass for each distribution are far apart, the estimation gives a wrong value of the expectation of $f$ : 1.127 in the last case where $N=10000$. The importance weights give too much importance to points bellow $1$, and does not match the distribution of $p$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3B - Adaptative Importance Sampling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we want to implement Population Monte Carlo. In the step (iii) we need to maximize $$ \\sum_{i=1}^n \\tilde{\\omega}_i \\log \\left( \\sum_{i=1}^M \\alpha_j\\phi(X_i;\\theta_j) \\right) $$\n",
    "which is similar as the previous log-likelihood of Exercise 1, but with weights $\\tilde{\\omega_i}$. We can proceed as a classical EM, but using $\\tilde{\\omega_i} \\tau_{ik}$ instead of $\\tau_{ik}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 287,
   "metadata": {},
   "outputs": [],
   "source": [
    "class GaussianMixture():\n",
    "\n",
    "    def __init__(self, n_components, n_iter, weights):\n",
    "        \"\"\"Inits the GaussianMixture class by setting n_components and n_iter\"\"\"\n",
    "        self.n_components = n_components\n",
    "        self.n_iter = n_iter\n",
    "        self.weights = weights\n",
    "        \n",
    "    def fit_predict(self, X):\n",
    "        n = X.shape[0]\n",
    "        d = X.shape[1]\n",
    "        m = self.n_components\n",
    "        \n",
    "        #init with KMeans\n",
    "        kms = KMeans(n_clusters=m)\n",
    "        preds = kms.fit_predict(X)\n",
    "        \n",
    "        x_comp = [[] for _ in range(m)]\n",
    "        for i,pred in enumerate(preds):\n",
    "            x_comp[pred].append(X[i])\n",
    "        x_comp = [np.array(x) for x in x_comp]\n",
    "        \n",
    "        alpha = np.zeros(m)\n",
    "        mu = np.zeros((m, d))\n",
    "        sigma = np.zeros((m, d, d))\n",
    "        for i,x in enumerate(x_comp):\n",
    "            alpha[i] = x.shape[0] / n\n",
    "            mu[i] = np.mean(x)\n",
    "            sigma[i] = np.cov(x.T)\n",
    "        \n",
    "        # EM loop\n",
    "        for k in range(self.n_iter):\n",
    "            sigma += 1e-5 * np.ones(d) # to avoid singularities\n",
    "                \n",
    "            # Expectation\n",
    "            tau = np.zeros((m, n))\n",
    "            for j in range(m):\n",
    "                tau[j] = alpha[j] * multivariate_normal.pdf(X, mu[j], sigma[j])\n",
    "            # print(np.sum(np.log(np.sum(tau, axis=0))))\n",
    "            tau /= tau.sum(axis=0)\n",
    "            tau = self.weights * tau\n",
    "\n",
    "            # Maximization\n",
    "            a = np.sum(tau, axis=1)\n",
    "            alpha = a / np.sum(a)\n",
    "\n",
    "            mu = np.sum(tau[:,:,None]*X, axis=1) / a[:, None]\n",
    "\n",
    "            Xm = X - mu[:,None]\n",
    "            cov = Xm[:,:,:,None] * Xm[:,:,None,:]\n",
    "            sigma = np.sum(tau[:,:,None,None]*cov, axis=1) / a[:, None,None] + np.eye(d) * 1e-5\n",
    "            \n",
    "        self.alpha = alpha\n",
    "        self.mu = mu\n",
    "        self.sigma = sigma\n",
    "\n",
    "        return np.argmax(tau, axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3C - Application to a \"banana\"-shaped density"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We used $d=2$ because $d>2$ lead to the apparition of NaN\n",
    "\n",
    "The coefficient before the original $\\mu$s and $\\Sigma$s where chosen empirically "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 266,
   "metadata": {},
   "outputs": [],
   "source": [
    "d = 2\n",
    "sigma2 = 100\n",
    "cov = np.eye(d)\n",
    "cov[0,0] = sigma2\n",
    "b = 0.03\n",
    "\n",
    "def banana(X):\n",
    "    new_X = np.copy(X)\n",
    "    new_X[:, 1] = new_X[:, 1] + b * (new_X[:, 0]**2 - sigma2)\n",
    "    return multivariate_normal.pdf(new_X, np.zeros(d), cov)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 267,
   "metadata": {},
   "outputs": [],
   "source": [
    "def adaptative_imp_sampling(n_components, n_iter, n_samples):\n",
    "    alphas = np.ones(n_components) / n_components\n",
    "    mus = 5 * np.random.normal(size=(n_components, d))\n",
    "    sigmas = 50 * np.stack([np.eye(d)]*n_components)\n",
    "    \n",
    "    def likelihood(x):\n",
    "        p = np.zeros(shape=X.shape[0])\n",
    "        for j in range(len(alphas)):\n",
    "            p += alphas[j] * multivariate_normal.pdf(X, mus[j], sigmas[j])\n",
    "        return p\n",
    "\n",
    "    for i in range(n_iter):  \n",
    "        # sample according to q^(i-1) and derive the associated weights\n",
    "        Z = np.random.choice(n_components, p=alphas, size=n_samples)\n",
    "        X = np.zeros((n_samples, d))\n",
    "        for i in range(n_samples):\n",
    "            X[i] = np.random.multivariate_normal(mus[Z[i]], sigmas[Z[i]])\n",
    "        weights = banana(X) / likelihood(X)\n",
    "        weights /= n_samples * weights.sum()        \n",
    "        \n",
    "        gmm = GaussianMixture(n_components=n_components, n_iter=1000, weights = weights)\n",
    "        preds = gmm.fit_predict(X)\n",
    "        alphas, mus, sigmas = gmm.alpha, gmm.mu, gmm.sigma\n",
    "        \n",
    "        plt.scatter(X[:,0],X[:,1], c = [[1,0,0,weight/weights.max()] for weight in weights])\n",
    "        for j in range(len(gmm.mu)):\n",
    "            confidence_ellipse(gmm.mu[j], gmm.sigma[j], plt.gca(), edgecolor=\"r\")\n",
    "        plt.show()\n",
    "    \n",
    "    return gmm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 268,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm=adaptative_imp_sampling(3, 5, 200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 269,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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j+iNU7XXuUkQU+v8ZGbGpDLljB9Gvvxof/qpV8MsfeGBk3ZLatUOv0SFDiC69FKUIHn2U6Moro9OFSUg6ouFaOYyITlNKbSCi/xHRUUqpl4OfpLV+Wms9Qms9orS0NAqHFWJGWRl6Oj7wACzeK69Ebe0jjkiOCA6XC+LN8d+ZmfjpdEKIlcJjJSXwI+fmwlotKIAoW2PMPR7jltHaTAxVVbDAXS64j+rqkDK/Y4dJ9Y8Ev59oxQqMq7AQdxQdOmAS2rEj8v1v3Up07bVE77+P9Yz338fC6Lx5ke9bSDoiFnKt9c1a6+5a695EdC4Rfaa1Pj/ikQnxZ+1a+Fb33x8CtmgRelI+9ljs6n60BZersdVst0NgtTaLkjYbfOs5OcaNwmGGHHrI8eQ+HxZCuclEQwPcLNu34zn9+2NS8HggtK1d+NQ6sHlFQwP2FWwh5+ZiYTUSvF5EsYwfjzj+/fcn+ugjovvvRzLWySejpouQNkhCkAAf7d/+hkWybt1wiz9tGnzjBx6IAkuXXBIY3pdI7PbGQsouFIcDP61j9fuNlZ6RAddDhw7YSkqwv927TU/NXr3gS+dEon33hcASwQ3CES/hUl2N93T1agjojh1mYgk+D7fbHKstaE101VXY/223mceVIjr1VISIHnUUGl1cfz0icoSUJ6pCrrX+XGt9SjT3KcSQnTuJbrgBpWJLSiAyd94JgbMyaRKsxKlTEzPOYLKzjfVNZKzdnBwIVmGhcYtw1Epw4wpOySfC/63WscOB96BbN4hqcDXE4ImiOZxO+KgdDowhPx9CXlWF/e/aZfbFVnqXLm1/b+67D0W33ngjdH9QhwP1bpYuxdgGDEB/0Wi4i4SEIRb53khlJay1AQMgHEuXQgDatw/9fIeD6PXXIeRffx3fsYYiMxOC6PNBwNlyZsFl/3hREbaSkpYX+UK5SthvHuq54TRR9vvhmuGSukSYBAoKIOB9+xL17Gni1H0+3AHl57e871C88grKK3zwAY7RHB07Ej31FFwuM2einPCnn7btuELCSZKW3kJcqKtD9MLUqbjNXrQI7pNw6NkT2Z7nnYe64cFWe7zhphTsUglehGVXSjjY7ZgE3G4TdsgC3qkT3jcOQ3S7IZL8vKaoqoJAb9qEv0tLjUDbbMbds99+EHRuOdfWxeT58+EqmT+/dTH9w4ahFvqsWSimNXQoUv/79WvbOISEIBb53oDLhbhwbl785ZfI9AtXxJmTT4aQX3BBcvjLlYIoRiOSprgY+6mvN1tREeK6O3aEcGdm4veSkub3VVuLcMfsbDPhlZebLkVuN/7HVnpGBv5u63n89hvROeegLPDgwa1/vVJo7rFsGdEhh2C78cbEN4gWwkaEPJ3xemFF77cfbqHnzIGLJJKmu5MmQajuvjt640wGMjIg0h06wMXUuTN82kQmNLBDB+OHb47KSjzPZsME4XDgs9i1C9Z9Q0NkfnArS5eiyNnDD2MRMxKys5HstWQJxtq/P9GzzyZXnRkhJCLk6Yjfb6yzl15CWdnZs+EHjZTMTPhUn3+e6OVG6QKpjVKmQxBXS2wLHo9ZSM3IgFuK0+NLSnBnFElkCrN0KcoOP/AAui5Fiy5dcMc2ezbRCy8QjRhBtGBB9PYvRB3xkacTWuPiu/VWCNJjjxEdc0z0k3i6dIF1f+SR8McefjgmD/YjJ0PSUFvQGn5ta7Gw7OzQJW6bIy8P++DF14wMCDdb9dHgt99giU+ZEl0Rt3LQQXDDzZwJd9rIkXDRSc2WpEMs8nThs89Q/W7iRLRV+/57WGuxEtVBgxAlcc45RF98gXKvS5aYNHMuI6t1YIOHZIbdHjk5ZnO58Hhz+HxY3Ny6FYubbrcptMVNMLQ2tdAjZckSfLZTp8ZOxBml8BmvWIE7iWHD8LknWyXIvRwR8lTnu++Ijj4aCT3XXEO0eDEKWsXDKh42DGGMF19MtH49jslt13bvhnXLLdl270YoXjwX0LTGeLi1W0vU1eFOxkpWVvNC7vdjIbO+3hTx2rkTFrzHg62kBDHj0ahz8uuvsMQfeggLz/EiJwdlcD/4AKGq48Zh4hKSAhHyVGXdOlxMZ52FCoXLlsE6i1dFQm5i/Oc/w2KbMAGP2WymQuG6dSZ0jy3cqqr4lIP1etEnlJtDbNoEwQ3XkvR6Mens2mUsa25KYY3YaWgw511XB7dKcTGO0749JgKu8RIp339vFjbPPTfy/bWFESOIFi7EJD5sGGrQi3WecETIUw2nE629/vAH+CxXr0b8b7yr2lkv3vHjsbB6zTUQOo8HVum2bRDB7dsh4FqbWuKxhpNsqqqMm2Pz5uat69xck2C0axcmKo8HdxqrVmFCKC/HefF+uPyt2x04iVrfn2i4lN57D7H/M2Zg4mwJlwt3QeXlTTcIaStZWXDfffghmkOfcgreGyFhiJCnCloTvfMOBHPFCrhQbr65cfp4vOCKgZzIMnEifMDXXAMB5FjpvDwIJPuf4+Hy4YxKj6exv7u5yoL5+TiXXbtMgSsuuOX341yzs7FVVpriXdykwireHOPOCUuR8NRTRFdcAbdGOI2TKyvRVILdWxs2QNCjzQEHoBzAwQejzPHzz4t1niBEyFOBVavQb3HiRMT1vv46UY8eiR2TUnAdcIie1phY8vNRYc/tRjYjW6PcM9PjiU7oXUvU1kJw/X5TGrampnkhVwoFtfLzMXZ2jbAvuK7OCDPfWVgTe7Q2Lqe8PBPJ09a7Ja0RgTRlCqJH/vCHll/j9WIS4wk0N9eUBAhnnaC1OBy4Q/zkE2QNn3iiyWYV4oYIeTJTWwtxHDUKUQq//IKFzWQhKwuhiO3bI0u0Xz/U+nA4MOnYbMYVUVsLgSssbLygGG24fG1DA1w85eWwmuvqIOaVlc2/PjcX4rxrF1xX27dDnHbtMm4KLpxls+H8ue55fb2JRVeq5SzQpvB4sIj88cdE33yDNP66OkxEO3aYScXvxzErK/EYu62s4ZIcEhqL5hjMsGHw4Y8ejXoxzzwj1nkcESFPRrRG7O7AgfDrLlmCinXJ2N0lIwMixtmQffrgFtvjQWXFkhITV92tm8mWjAVOJ0S3vBzjcTrhWuAIkvx8jIGFnftx8mJoZSUeLyiAWG7dit+LivB6rc2CKbttiCDaRUWYzIYMQWw9F/HibkatoaYG/vDycoSVlpZibFxqVymcV3k5Jir253OUUFM++VgvhGdm4g7is8/gDjr+eDTlEGKOCHmysXQprO7Jk4lefRWZmdFK526KaNdNycxEeJzbjUJOWpu637Fi2zZEyVRWQszKy43AsnuhXTsTy+3x4Lm7dkHovV68ftky/M5ukaoqTELs7+YoFm5YYYXdOOXlOHe3G8eoqQlfzNetQz5A794oZJWXh7FyRAyX383NhYjX1uJ3h8OsBXDTacbjwfiDxxsrhgxBWOxRRyHKZfr05KjNk8aIkCcL1dWwuseOJTrjDFQmPPzwtu3L6YQlxJEWTYX71dXBEv3995YjOsKFb/d79kR6t8eDWPOiotiFHTqdEFgW7fx8hADa7ZhAOnRAFcOOHU1TCm7nlpeH976iwvi916/HWLkqIu9r1y4Is82GicG6iNnQgFDHlSvxvIoKHIddPOGk+3/2GdxoV1yBGuHse2/Kwm5oaHyXlp2Nc+Y+ptw0ulu3+DfLvukmJIs9/zxcg+vXx+/4exki5IlGa9QsGTgQIrF0KRYL2xp3XFcHq45LsvLfwSJaVwc3BKeP22z4O9iP6vOZtmjhWFVKmSiPoiKTBXj++bFZbONzCdX6LTsb70F2Ns5RKQg1W7ZEeF+cTvzfbsfzOQmooQH7dTphzXLvz9xcI9REeI94HUAp7Ke2Fo/5/fi7OSHXmujxx5Hg8+qriMkPboIRilDRMFpj/H36wKrv2RO/x8saD2bQINSwP+EELNY+/rhY5zFAhDyR/PILutI/9BDRW2+hUmHHjpHtc9s2XLTZ2RAArsIXHH5WUWGeQwTBysoKXAisq4OfeOdObFu3hifGBQUQwdpabPfcA7fGOefEprVYqNZv/Hj37jg3XggsKDCWOREE1u83LhmOEc/KMmGGlZXGhdG+Pd5P7ipEZEoQ5ORgvzw58mTg95smGMEiVl+PNnrTpxN9+23oCoaZmRgPZ81yxmpJSWCPUiJzjjabOYdE177JyCD6v/8j+uorTOzHHIO7FyFqiJAngooKWN3HHQdL9YcfUAM6Uvx+iEpw04NQaebcPd5KRoYRaq8Xi2ta47WcYLNxY8sWFUd97NwJYbHbie69F7HGRxyBuOa6OohYNCIb8vNN6B/DRasKCuBW6N0blmlpqRF+pXCOO3bgfePuPTYb3C4soHY7rPju3U1PUGvcOB+XLXp+D7nJc0UFzrWmBsfju57ff4f7rL4ePuW+fUOfH4d65uaau6PcXIynpMTUT2cRb6k7UKIYMABhlGPHwncuHYmihgh5PNEafuOBAyGky5ahRkq0fJc2G8Qn2Kfq8TROHMrJaWxdc99LIiMYFRUQORahVavg62zOVeD1YuvVC2LDIYr/+heaU4weDetz2zb48CPNfHQ4cCyXC/7u6mq8Fz16GGvUbjchebW1xq1kt5vM05wcExuvNf7u0gUTQVERzt/aho0nQg6n9Pvxf4cD753bDXEtKTELkg4Hjv/RR8jMPfdclBnOy2v+HLm2edeu2NhvX1iI8XXsiMdLShJvgTeH3U70739jEf+CC1DXXlwtESNlbOPFli1Ipd++HRl6Bx0Um+N07IgFzNxciDqHpXXrBjFmX3BJCW5vOTqDXQzFxdiP1hDE3Fy4Zdh3zFZ/eTkWEIkaCwcLc/DjHg9qs3Tpgp8vvEC0//6B+2oreXlooMGWdVMZr16vEW2lYKEPG4b3ht8Hux2hlCUlEGN2zbBgNzRA2HkCdjjw3Opq41ohwnNycgIXJH0+1A9/+WW4GVrbDCKUSNtsLbeeSzaOPho1W847Dy6Xl1/GZyG0CbHIY43WsD4OOADuk+++i52IE0E8evSA4O7eDfcG+6xXrkSrt/JyiA13iff78bNbNyMImZnGr8vp5j4fHrfZIFqbNsGq3r070Kq227FPpxMCyP+rqYHAnnsuCj/99a/oMel0RqcLDYfYZWebyJRgeNGXBZFLDbRrByFhq9Zmw+RQWgqXzIABmOSysvBca3YqTwgdOhhrPC8Pf7vdmEg9Hkzmp5wCAfv668g7+qQ6XbvCvXLggdiSobF3iiIWeSzZvh2uk7VriebNw5c1HnD3+PJyE8PM4u3xwM/N7caaanSQlQU3w44dZpGNCJOC14vHCgogmh4P/Ofsf/b5IO4ej5kY2G/OVu0xx8AivfBCCPutt8JNEA3LsqEBdyJ+v1l4ZKs4uEFEZibcIRy+yAuTvHDJ1NTgtXY7fnc6jauEXTTt2pneniz0Lhf2+e67CMe78kqiv/8dzw3nHDgKhRet042MDKyfjB6NvqE33ohEsmR2DyUhafjNSBLeeAO37IMGwQKLl4hbqa2FCGzfbioAEkGovN7ABdDgRUeljNDn50PkSkrMZMA+XyIIF0dS+P0Q/y5dIFYsPnV18JdbLfc+fWCZz50Lt9OKFZHXK29oMOGI3JW+utpY/Dxm6x0AR6PwJNOxI+5OXC5TRVBrvBc2G95L7r9ZVRWY8OPxBJYgyMpCctcttyAqacKElsvacikBmw3Pa2jAOaRzyvvJJ2PRf+ZM5FHEIropjREhjzbl5bAwb7sNVtg998S+tkhT2O0mhZujLHbvNv5g7tpTUYHQwu3bTQ0PIghcjx6wtLnGCLtirCLNx/J44ErQGgJUVARB79oVQpmZaRYNOROzTx9UdXS5iC69FC3M2rr4qTXOiSNLiIwVzS4Vux2CzMWt2OrltPrcXHP+JSUQ3bw8iHtGRqDA+v34bF0us/hrDYVcvx4CVVaGminHHIN9WmO6tTZZoH6/qZ2SnY3jKGWaN7e1h2iq0KsXolp69YL7cdGiRI8oZRAhjybvvWdqbfz8M6ISEkl+PmKgOYSOIze4EqHNZqricblWrt/NZGcjLG74cITwsTXJqefsh/Z6jbXb0EC0Zg3eg2XLTC1y/p/fb3zneXlwqTz1FLIazz6b6Kefwj9HdoVwPHWosr02m+kAACAASURBVLGcgs9kZWExs7TUbLwWwD5zrs/C7hOl8HdFBc6nqgoTEi+G8kSRk4PnvfYaFvROOQVJML16Bcbt83u2e7fZX3l507Xag8+B8flMWYCqqtQXe4eDaNo0LAifeCLRE0+k951IlBAfeTSorCS69lqsvv/vf0jySQaysmABcmo5x1XbbEaArK4ArhpYUwOBtVrcmZkm1by4GM+pqoL1WFCA/2dnQ9BWrcI+8/NxnBUr4FbJzMT/2ZfMwsh1S268EXcAJ5+MiJaTT2763LgXqHVBk61krhPOFq3X27h0Lpei9XgghJzFmZWFn9Y4cb6TKS+Hi6NDBxMZU11tQg7ZrXTllcjQffJJTOx+v1kA5UlGa7x/PLHyY02VSWB/vxV2+/Drd+/GgmqHDvjcWyqyxsW/+L1LJh/8mWfCNXnWWbDSn3225RDNvZgk+uRSlA8/xMWan28yNZMFLho1cCBKzHLUBRF8wPwcK0oZH7r1tt/jMeGLhYUQC05Qycw0GY/bt0NE2OXg95sMybo6I6i8eGezYb9EOM7xxyMU7bLLsAjG1QN9Pmz8N7si+E5DqcAQwvp6UzyqqfA87qnJVrjdjjFaJwhu7+Zy4fh2O1wlnDnp8Rgf/PPPYy2kXTuk2g8fjvMsLMTzrGUS+Fys7z+n97MryOp3t9uNMPt8eD+3bsVkwMlaSuF7WFtrkpA4Jj7UuXM/1V278LnFowVfa9h3X+QbZGbiupIuRE0SsUWulOpBRC8SUWci8hPR01rraZHuN+lxOrG6PncuLuBjjont8bixr9ttxLSleixcZ8TlgtC2b4+LOyMDr+fICBYItxuiVFcXGL3BbgWv1/h3s7KM1c3+XCKIKUefcMJRZqYpHcvY7XBBbdpkwhLr6zHGjh2xvnDZZbjLeeopiCPHujscOCdrrLjXa6zKwkIz+WRlmVoyRCYD1OcLzIJl3zQLNzeE8PmwD4cDvxcVmaxUXoRUCouYK1agFVvHjvj/tm2Y8Gpr8T5Zx9ycu4DrwnDkjTWRKTsbx+euRLm5GIM1mcvlMmsfxcV4fVGROVePB2PjSZtzCXbtgsuJ7yCIcLymLHuXy4yFa9FE26rPySH673/hahk5EhUhw2mwsZcRjXfdS0T/0FoPJKJDiOgqpdSgKOw3eVm2DO2tqqrQ1TzWIl5fj+qEXE61qgp/h7MoyKndnMKdkwNRrK3F3xzl4XZjYbShAeLD9UO4ZRtb1U6ncUWw2Fsv9Lw8429msWcxZDHjGHOelPr2hahzHDtXT3znHQjQ6NHwtxMZdxBPLlYL3eUyi61ZWUa8rCLOzZKJ8DO43Kt1kZQIz+ckHz4fDtm02yHe55yD9/S113D3U1cHdxOvSeTkQFStvnuedKyTG8e+c0ladkHx3RH3Qq2uxnvObea0xrGqqiDGmzfjs2poMK6iysrAhe0tW7DYzHcTHNW0ezes84oKbBzxFAzXfufPs6ICY+MF72j0KWWUQlbwY4+h1d3MmdHbd5oQsUWutd5KRFv3/F6jlFpORN2IaFmk+046tIb1feONRPfdhyiLeMS77twZ2FIsNxcXUnV10/HILLJ2O8ScO9XwAhtHc7B1W19vMj7ZxZCfb+LFucHwunXYHxH23759oNuic2eICReZcrvx+777wjrcvBn/Z0szPz/QR8zC5PebC/jzz4lOPx2RQJdcEvie851Cfb1JXOKGyNzsmbHWRCHC//x+I/7sArFmsXLvThbysjIca8cOuE9++AFFz4YMMZMs3wXxOfFkE+xGKSzE81mo+RzKy81dANeMYbKy8JrCQtOHlMiESnJcPP+PP0civO9EZn2isNBEyGRnm4XvrCzzXnFf1uCWdhUVgbHtdjvek8pK4z7jcsLRukbGjUOU02mnwZi6/XaJN99DVBc7lVK9iegAIvo+mvtNCmpqsIj188+osTx4cHyOy/7q4BBGhwNiHkrIa2pM3DELBhdSYmuORSUvL3DRMzPTCBvDt9pcVIoXSrlMrPV2OjcX782mTThWVhayIln8O3UyPu3sbHNenN1pFT0W9uOPR2bslVci+++hhzDhcEVDLvbFdwHWxU6rCFrdFPwe8gIuuyrYHcVwFIrTCXeEzwfxvv9+osMOw3chJweTLb+nvMhbU2Mm0+LixpMK9zDluyVrfL7PB2EMLjXAC7H8eXGjjM2b8XtBgXERcUEt7h9aX4/HrHchdrtZ6OVF3S5djJvG48FjHH7JYw9+L51ObFwTnr+HGRnRLeLFLeXOOINo+XIsiieqRG8SETWHllIqn4jeIqLrtNaNsjqUUuOVUguVUgt37twZrcPGh59/RlxrTg7Rjz/GT8SJTORFcLq5NdzPitNpIlRycwNdIn6/WTizwgk9ViuMLVs+flmZyWbMyTH1RUItpuXlQbxHjMCFxyLO4y4ogLBxiVVe5OP66Xy+DQ2m680++2Bh2eFAavuyZcaiz8rCMXNyjKuC/cTW9427/Fj/5smEfcFW4fT5TDIUZ7hOm0Y0dSrRnXei+xG/fwUFpnMQN6XYZx8IYGFhYHap12sqLrJbg+u/sMXNfuvgKBaeTHnxVGuMcb/9IMAcKllYaD5XosCoF14jcbvNOgnH31sXVfncrCV7+X0LprYW+7W+NifHLGRHk86dUdqBF0GlJG50hFwplUkQ8Ve01m+Heo7W+mmt9Qit9YjSVCmOozX8cscdhwv3mWfi0wHeCnd25wVIIuNOYGvMCosJ33Ky5VtTY1wPwcLLgsUWqt9vLkKHw0RAcI0RtqJ5n00R6oLnEEErfOfATYw52iI7GwLN9V0yM9FR/oYb0KjgrbeMC4LDCfmcOXWeFz2JjJVvDSvUGufERbD4+WzxsgW8fDlKDns86Bh/4ommVC9HxnTrhq1vX7xXSpk7hfbtzXtVV2cmLm5qwQ0s+DycTtPz0+pvdrvxnnTqZFwoJSUQcU5c6t7dxOoT4TNlVwy7nYqLTYkFXggvLMTf1uPxZG5dWLfbcWynMzCyRqlA65jXACKNA2cjwzqu7GzUMDr9dNwZrVwZ2TFSnGhErSgieo6Ilmut/xP5kJKEmhp0MV+/HiFQ/folbiws2BUVZjGsa9fQGaPBi49EJrmFrTn241pDDYuLcbFyNEZRERJltIZY9ekTuOjlcGA/VoEKh+xsCABHmXA8OHft6dLFJAv5fKYAFgu53w8/+QEHoAzqN9/AzWFt9pCVZcSHC3ixK4BDBq0p+1aXCAsPryFUVKAOzBtvIBzyhBPMuXC2al5e4yYOxcVGeII/D3b9WBc3rS4tvhvy+81nwNZ3djbGGdyDk10kvDjLvT6LisxkmJVlood4gZLDLx0OWLo2m3GT8J1Shw6Nv2vs+66tNZOhtfIjn6c1dr4tcL9Sngz43Ng9d+utmLiOOAKL49Go65+CRMNHfhgRXUBES5RSi/c8NlFrPScK+04MK1fCBzd6NAo7JSrF3kpRESwmvtCbIi8PYmwdM0eHEAX6L9kX3a6dEZvc3MZ3HZyIwRcukanX3Vr/Jy+o1tYGNnNglwYXuWKr2Jpt6fMZQR8+HIkiEyYgamjGDFzQLNYszjZbYCd7/n+oDFA+FhFe8+yzEIo//hG+cOvzWQy7dg1dMtd6h0CE8+XIEV48zMszUSncNJnj5dktwgvNfBfT1Gdvs5myu2y184TGZGZiYqiuxiTcu7eJEuL3muuZWxOXeJIPPr/iYvOdJMJiKTcS4QXiwsLQ4w0HdjtlZprx+HwQdut+L7oI53XqqS0nkqUpSicg/XXEiBF64cKFcT9uWLz3HuKXJ09GIadkxBppwWFojNcLC5pFmhfxrO3NiIxbIZy434YGLHjl5AS2LSsuDmy00Fr4u9dU70m+W+CwQhZH9mezZf3ss0R33QW3yxlnmPeDBcDna7wo2xw//kh01VXYz2OPIcnH7zcNKIjwv06dwpvIOCyQU/RramAN9+yJMe3cafp91tVhrPvsY95vntyaakDCUTu8KM6x/02xa5eph8PwnUhpqYliIjJ++3Dg8E5eDI+0YiPfYQTf0Xg8ZoKz8v33cLVMnUr0l7+0/bhJjFJqkdZ6RPDjkqLP+P3oVvLssxDzZL1F45KxVivTKqgZGRBtzmrkQlDBF5TV6moKtxvRJzt3Qly4jRhbipGmTDd3fLaO2cXASUdeLyxbtuIzM1EW9tBD0axi3jyiBx+Em4DIhDGGIyi7dhFNnEj0/vtwo/z1r+Z1NhvcPqWlZiEyHJcB14W3fgaFhSaWnssT1NfjObx+VFaGOyX+X3U1PtdgUXO74S7hc+QImOCiZlaCKzQSQRS5rrzPhzFam1SHA/vI2xJF4nKZPAlrElJTk3woRo4k+uwzRDlVVOBubS9BhJwI1tBFF+Hi+fFHIwLJBtcVt9vNhag1hI2LOzHsmuAY5eDaKRy3zBdPTg4iQT74AG3I1q6FsHXpAgGprET43THHEP3nP3g8HlhrmnPkDZ8zh7plZCDb75df4AoZORJjHDeusd82FD4f0dNPIy75z3/GwiZ3SgqmpX2F2jdRY1HlMMOOHZGg06OHEU12e/GEwXcfVVWN68dzb1FrbDx/rk0tzGdnYwKwZrWuXo2NKz7m52NsXbqYjF/rBB7N+G0u38DrBpwfwedihdc6mpqkBg2Cy+3YY836xl4Qay5CvmEDbscOOih5/OFNwf7V4O40XJvD4TDJGvyFV8oIIC+ashBWVWGx8MMPUWY1NxfJFrfeigzFrl0DLbKqKli7p5yCCY99t8F1QLheic1mQiDbejGxL5szCK2LhOxi4s8sNxcCfuaZWKieNQuukeaipL75Bm6UwkJEowwd2rZxNgW/f8E+eXYPcESGdRKurw9M9iEyombdDy/uBlvA/FwuOcxuOF7YLSgw0TZ2OxqNrFgBV092NiaB2lr8jw0Bfo937sS+oxV55nYH1uAhwpgrK+G64jsSLmLG9WSa+z717g0xP+44vHby5LQX871byH/4ASJ+001E11yTHh82Z1Ja43452iMvDxfD22+jycF33yH647jjiK6+GhcyN08IRVER0aRJuH2dNw/uJ77AeOGzshLP5QVFLnXbVjcMZ56y35XI+II5vDB48h01imjxYjT5HTKE6NFHUUXPyvbtyBr9+GNMTuedF5vPnxchy8tN1yG+C2JB4rUMFn1+jnX9wToxM+weC54krPVoduwwC6VKmWJnpaUQUK6t07lz4II4i3lDA8IpmcxMPG79PK2Ly62FJ5Pg94wnOHazeL3G3RaOm6xzZ7SRO+oovP7OO9s2vhRh7xXy2bNhtc2YgdXuVICjNzh0j8gsCnLkBNdOsVotbjfqg3/0EWJv+/aFC+HZZwNj0TlBpaULpbDQpGgz9fUmkoOFlWPYucZLWxa+gsMFiZqPPGFyciDQf/oTPufXX0dd8Pbt8XPSJDy+YkV0Mw9DwR3vKypMOVvutsT/ty6GOhzGIiUyi4hcZoHhvqK1teazsBY727EjcDHc74f7sFMnHItj54uKTGKXNVqFM0GDaWhAqQb+ztlsgRNBa7BG5ATDY+GKkK2ltBRifuSReP2//936faQIe6eQP/MMPtTZsxPf/KEluFiS222sO25owNaYNf2bLXHOjpw/H9XjlixBf8z589HkoKamsSUbThSL348uPpMmBT7ucJjKh029ri1CzrfSNpvpZM8LjZw01ByHHILM3DvugLuIsyAXLMDf8YIXikPBPueqKrNAvd9+JuOSyGSHhtqv1qYhBYcQsvvJKuI7d+K743Sahh75+cY4qKgw4u5y4XjBY+bSAV27mjsGnw/rJ716tV5w+TtovSNh/31L9dTDoWNHiPnYsTjPiRMj32cSsncJuda4oF95BRfyvvsmekTNw80HnM7AjMz27c2iX3D4IS+MPfUUijrl5yMjcfp0nC9bQLW1gUk5XAa1pQtxwQJcfH36NP4fx3pbx2NN5GgrSpmaMHzXwH7bcJo1l5cT/f67WUPIzw9taSaSUPH7xcXmDqmpSVApU2OF1yuUMmVoGW4CkpuL88/Lg1uF49tdLvy+fTv+164dYvW5SiaPrbrauIUY/k7x3UZr4ISjigpT9jgrq+nF5rbQuTPcgSzmN94YvX0nCXtPYwmPB9UK58xB4aVkF3EiXFzsluDMwYwME27GmYtMeTmqMh51FDrUTJmCULoLLgiMI2fLnn2xnDAUjovhgQeIrruucUsxjivnNHd2+bhcLS9OhQuXwmUxamlh2u2Ge2XYMLiT1q6Fi2nwYDz28svJ3UasNT5hzmTl95nLFvCkx6UbrAuXfj/CS3v3Rm2cvn2xTtK7N0SvsBBumLw8U6CMI22sC67BnZpaC++ztBQ/27ePbOIPRdeuuBt95hksiKcZe4dFXleHxS6l8GFGksQSLThe19rqKxhuAhH8WHm5cVVwZuDDDyOEbtw4WB+dOpmIgOpqWCUc2cICUVxs4qzDEdpff8Ui4ptvmmJL7N7JzTUx69awxqKi6EYChSNqWmPC/uc/cefw7beBE/fkycjWvOgi1LaePh0Xejphs0EYebGTI5fatzffKb7Ts9sh2uwWq601wmy3Yz9c+ExrRHpxl6KdOwMnbG6K0VqspYi5f2y06dYN18YRR+C7f8kl0T9Ggkh/Ia+tRcpunz5Y3IvFF6Q1sHVUXW3+5sWvYJEKLnDF9aWt9aMffhh9Qs89F02Le/Uy1fWqqkxTBy6pmp8faHmH67f2eIjGj4ePkd0A3NjBGqvNbpBE9Vf8/HOMsboadw+nnBJaWLhL+6RJcCE8+CASgNIhconJzoZ48XqKxxP4uXAqfyis78OuXYHx6506IeZ882bTjJvr0GdlBVa7DIeqKsTSs1FAhHHHYhG6Rw909RozBiUdjjsu+sdIAOntWqmtRUeRffdFdEqiRZwIVkdVlRFDro1S3ajyr6lWx19ubv1VVUV0yy1YyPP7sZjz2GNI3uCWcGzZcEVBjvrgglWt5ZZbcDFfdZV5jAsxJcP7+sMPSAK57DKM8ZdfEI3UnDA7HEjt//BD1Dg/5RSIUzpht+N70K0bPit2kdTV4fNkdwvDXYX4LnHKFBOqyHDVxR49TLVF9rvv2NG68Xk8EPG8PGNk5OYiusYaqRRN+vdH5czzz8f3JA1IXyGvqUGp0f794XJIVIfwYB9sbW1jV0N2tqkiZ4VrfnPNibVrie65B+fl9+M2cfJkXEy7d2PBqLISFwH397RW+eMFsNZeIHPnwup/4YXks1iXLIE76U9/gvts+XLU2WiNj/WAAzARjByJ3599NjKfbzKSkQEx79wZk3uXLvCFd+4Mka6pMQXRrFm7116Ln0cfHbg/7qjEi9B8jKaaPTeFtbMTY108jRWjRyO/IE0m7/QUchbxgQMRvZEIEeeaKFu2QFhZqNknbaU5ceTMyKlTic4+GxfO7Nnw/+blwZrhuuC8GNrQgHCw8nIIPNcyt9YNCZctWxBv/corjdPDE8nq1YiFP/ZY+DxXr4brp60haw4HQlI//RRCfsghyPpMJzjTlmuT83fG68V3dMeOxndYmZlEjzyCglTLl5vHuU2clfp6rIm0ZrK3ulOCH48155yDRMCTTjLF0FKU9BPy6mrUjN5/fyxiJULEOdaW06czMyGoNTWmAbEVlyt0xTq3GxfRwIGwtn/6iegf/0BoGFcv5JA8tkC50zon4NjteKy+3iyOhit2Ph+s2wkTiA4/PPL3JRps2oSqlIceiroaq1ejU09L8eThMnQoBPyaa3Ch//nPOGY64najvk59PazwkhKEaQafLxefGjTIiG5pKb5b1dUwHHgNhpOYwoW/99a7RG5+EY8Wbv/8J77bZ57ZOBIrhUgvIW9owK3S0KFETzyROHcKd07hGGe2hLihA2c7NjSYyAFrhqXW8OENHozoi48/Rkp9x454XocO+FlcbC4orhLodptOL+z/5PCwoqLQXYWC+eorxNqeeir2ffPNsXmfWsOOHQh7HD4c579qFWrCxGJBzGaD/3TFCjQUGT4c+QecdJMucJMJDg/NyICYb9sWKGpKIWSXCJnBRPhu9+tn+nt26oQkptZOqOzy4cmgpgbf4W7d4nP9KoX2fZmZKNWRoiTBKlWU8PsRddC1K1KwEyXiRKbrihVr6nOHDhBXfp61AcB338Hqrq3FZHTssWYf/ByuiMcEp+3zQmfnziZJJyur5SL/69fDQvn5Z+yjrAxbtGN6W0NFBRbcpk/H3cHSpfGrTpmXh8XQSy9FXZYBAxCnH6u6LPGG48Kt8Hl5PIHfsVGjIK4XXoj3oaAA11o03G35+ai/zj7x1pRz8PlwV1BTg9e0pUZ+RgYmqAMPRDTL6ae37vVJQPpY5DfeCEvihRcSK+JEJrbbCtexsHaQLygwX9q1a+EDP+ssuA5++ilQxInMhWVdiLO2aWPLm4sasc+ce3A2hdNJdNttaJZ84IEooLV1K0QsURmQtbVY2N1vP3yuP/0EN1MiSgz36oXF3ldfRTLJYYeh+mOqU1DQ2M3H361ggdcaawdEuNbmz8e6idVvHgncwi243HJzcO2Y3btNP9ayMkz+raV9e9TjufxyGDQpRnoI+aOPoo72O+9Ez1caCdzNhRsZe71YcCwubvwlLS+Hj3fkSGQbrlyJRJVQVjC3ZfN6TSQLd3Xp0AH/694dP3nRk9Omm0pl/+03CPjKlQjF6tkTsdVdusCVEW+4U32/fkhA+uoruJV69Yr/WIIZPRrRLZdfDqvtwgtTu4N7u3a4U+N8A5cLIti9e+M7Si74NWoU2t5t3Yrv9CuvwK+eCOrrA/u9ZmZictq9u22hi4ccAjfi2Wc3nuCSnNQX8nfeQTeXOXPwxUwGbDb4s7kBrlKm6znj9yNdeNAgXCBLlyJWOyvLCHCoEDiHw2TatW8PAefUbIcDxywtNXVT8vND32pqjbDMI4+E22DmTCTI3HADjvvOO9EpWhQuHg8svv32Q13wefNgBffvH78xhIPNhiielSvhWhg6FCGgwREcqUBGBr5/nToZt8Z++4VuGlJeDuHmBJpHHsH1lpeHxeFYxXw3BzeatmJ1DbWF667DRPZ//xfZ2OJMavvIf/oJ1tHcuaGLOCUSux0WeKjiPz/9hPZkNhuSUYYPx+NOp6nnzbRvHxh3zlEDTYmsz2csEpsNvkMugcp3A9XVCNVbvhwF+AcMQEz6ZZfhwrzjDtTxjgcNDajO+OCDuBt4/XVEpCQ7BQUwIC6/HBf9oEHIJD3zzNTynzsceN979mz+eVlZCKctLkbtnpdewh1T9+64Q6ytDW8hPZpw4+hguF9tW1AKyYMHHYSaRePGRTbGOJG6Fnl1NcLDHnsMroFUoLIS/ueTToKQfvWVEXHuRcmhg1woa/du0w2nqgrV6bgJcKgvMcerZ2fji56dDeuEIy6WLkVbtOJiLKwOGIAY4XPPhXV59NFw7cTjvbj3XkzA77+Pi+ezz1JDxK307YsIo+efh2U+diwWi9ON0lJ8H51OE4r6yCP4jnGIbbzhPqh8N8HrQ4WFkY2npATGxYQJKRNfnppCrjXRlVfCLXDOOYkeTctoDQtm0CCEVi1dioI9Vn+5tY44w7VW3G7jo+SwwoYGPGZNpuBmAMH+cIcDF+Drr0NoJk5EFEhODvydp56KsM3yckyMsWTLFliw++yDO4KPPkKC05gxsT1urBk7Fq6pv/wFyWiXXYYJN13IyUF+htsNy/zKK/H4V1/BxdSWphKRYrfjjoBLDzQ0wN0TjUiaww/H53jrrZHvKx5oreO+HXTQQToinn9e60GDtK6ri2w/8WDJEq3HjNH6wAO1/v77pp/ndGq9ZYvWu3cHblu2aF1drXVZmdYVFYHb1q1au1yB+9m+Ha8Lft748Vr37av1zz+b586Zo3VpqdY33aR1z55ab9oUm/dAa62XLdP64ou1LinR+tprtd64MXbHSjSVlVr/859at2+v9f33a11fn+gRRY9Nm7R+/XWtX31V6969kZa2fn2iR6W1348tmpSXa925c/PXbZwhooU6hKamnpAvW6Z1hw4QyEjx+yGE9fVau93R/SLU1OBiLi3V+vHHtfZ6m3++1wux3rXLiPjOnRBhpxM/Qwl5sEjU1ASK/tq1Wh96qNYnnIB9MjNnat2xo9YPP4yfS5dG79ytfPON1qefjmPcdRfOb29h1Sqtx43Tunt3rZ94QuuGhkSPKDp4vZisli6FhBx1VKJHFDteflnrYcO09ngSPRKtdboIucej9fDhWj/1VNteb8Xng9CVl0Pgysth+UYq5n6/1m+8gYv3r3/Vetu28F/LVjlvbHF7PKEt8rIyTEDBx6+s1HrzZq0//RRW0zXX4HyZZ5/VuksXfElLS7X+6qvIzjkYr1frt97SevRoHP+xx1Lj7ilW/PCD1iedhLuep55qfBeVylx7LWTku+8SPZLY4PdrfcwxWk+ZkuiRaK3TRciffFLrI46IjuVcUwMxrKkxW3l587fBfj9Etanj//671iefrPXgwVovWNC68Xg8WldVGYvc6TTi6/PhlnbxYq2XL4fIl5VBsEPhcsHi7tBB6/vug6jX1WHc99wDcZ03D2I+a1brxtkcVVVaP/SQ1n364C5g5syksWSSgm+/1fq44/D+P/dc40k4Famt1Zor/1iNhXRixQpcS9XViR5Jk0KeOoudlZVEt9+OutGRhnfpPQuIwUkPGRmmb2AwTicyDLdvNxUHGb8fi4cHHojEnp9+al2RKbcb++U+mlxWlPe9cyf+5/HgeWvW4H+hUu61JnrySYQ3Pv00wuO4CcU11xC99hpixsePR+JPNMKrNmxA/HmfPoiEee01xBafdVZy1CpPFg45BOGmL7+MLNEBAxAd0Zb68MlCXh7Riy/i9xdeSOhQYkb//ojmmj490SNpEgWRjy8jRozQCxcubN2L/vEPhBw+80zkA9AaE4O1xyERYq+VaiyQLhfENDvbRJI404C3TAAAHWtJREFUnVghLytDhILbjYSWwYPNMVwu0/KsuRCt7dtN0SKmvt5kgm7caEIKiUw44eDBgfv0+xGR8tprEIiBA/F/t5voiitwDs8/jyiVK6+MLHNTa7RQe+ghpGtffDFCK1uKRxYMX3yB0rlbt+Lneecltq5NW9F7moD7fAjXa6mmTyry66+I2lm3LqHZ40qpRVrrRvHWUbHIlVInKKVWKqXWKKWiX0Js1SoI06RJ0dmfUghZCs7+8npDf0g1NQjh43BBpfDFvfdexD3/8Y8Iw7KKeHk5BLquDl/usrLQhfJ9vsCCV0xmpumL6XIFjovF29q1pb4eseCffIIJpUMHVAzcsAGWMSfenH02BKOtIu52I+PykENQpGzMGNSm4IQeIXyOOAKt6aZPxzZwIOLpm7orTFaUwqROhNDS775DiG0CjMSYMXQo8lVmzEj0SEISsZArpexE9DgRnUhEg4joPKXUoEj3G8D996NTSWtrHTcHW8guFy4clwuxsKFqkni9gTHfK1YgqeeLL5BMc+21gZYU99bMy8OEkZNj3BvBX25rVUQr3AszuG+n9XWcELR9O2Lq/X64Tbp1w3ls3Up0xhmozT51KoR37Fi4qFrLsmW4K+rRA806Jk5EmvrVV8emlOzeglLIIPzyS7jCXnsNrQkfeyy10v7/8Acktz39NIq9HXww8ibWrk30yKLHxInI3k3CuuXRsMgPJqI1Wut1Wms3Ef2PiKJXB7K2lujtt+G+iCZKQYCKi/GzpKTpCoE5ORB77lZ/2mmwat9+G4ktwdTXN7awuX1VsD/UZkMtFKu1zs/LzTW1ormIj9amr2JuLiyfQw5BDYyHH8b5tGsHS+/cc5F49Ne/4v3bf39U7wt3jaGmBq6sQw/FxZmVhbrU8+ejaFQqugGSFaUwyX78MdEbb+Bn374QDut6TLLy22+Y2IlwzTqduJM++uj0aZt3yCGoobRgQaJH0ohoCHk3IrK2FNm857HoMHMmFg5DFfKJBlw1rbnSmfn5+FIedxys8DlzkMEXqo4K77OpGhChRJR7H9bXY/N4UGPF4cCE0KcPhL26GheI3Y6U6c8/hyV+992oj8Jts154AWVpZ8yARX711ehFGU7HJK3hJrr4YrhK5s5FMa+NG1FWtl+/5l8vRM7BBxO9+y6yXhcvhqDfcQfKNSQrTz7Z2CXk92PMX32VmDHFgnHj8NkkGdEQ8lDmXSNfgFJqvFJqoVJq4c6dO8Pf+4wZKOyfKLxeWEVnnQXr9q23EG3QsWPTi5c5OfgSWyvCNTTg8VBRHEphUujSBe6jzp0D7w4KC1GVrlcvPKd7d6L33kNNFO4GbrNh39dfjyiCefNQFvfCC+Hba6nZxrZtOM+BAxHpMngwXEhvv430fYk+iT9DhiC65Ztv0CB4331RCzwZS+du2RK6AqJSWGRPF04/HZVBk83/HyomsTUbER1KRB9a/r6ZiG5u7jVhx5Fv3ow050TF265bp/WoUchc27Chda91OhH7vWEDtu3bW87uDAe/H7HhvXohppwpL9f6yCORvLB8OTJfhw7V+m9/azq+1+PR+t13tT7tNK2Li7W+5BKtv/46+qnOQnT4/Xetr74aZQ7OOkvr+fOT57N6+mmtc3NNTDlvWVnIeUgX/H6t99lH659+SsjhKVYJQYRSuOuIqA8ROYjoFyIa3NxrwhbyDz9MTPqv36/1iy8iCWDq1LYnOnAJgGglxfh8Wl9/vdb7749Jjlm+XOt+/VASgLNAhw9H1l2oC33lSq3/9S8kBB16KDI9kyDZQQiTqipkyw4apPXAgVo/+igeSyROJxLhcnIChfzaaxM7rlhw/fVa3313Qg7dlJBH7FrRWnuJaAIRfUhEy4loptZ6aaT7JSLc2se7sUBFBRYy77sPoXw33ND21nHc7CEabgm3G4uWP/yAxZZue5YhPvoIIYATJyIEsKoKETXHHBOYPFVXB9/5mDFYc/D5iD79FLftl14qkSepRGEh0VVXYYHxyScR8dK7N3IDlixJzJhychB2eOedcOVxOeKtW9u+T86XaGhITOOKphg8OPmicUKpe6y3sC3yK6/Uetq0tk9frWX+fNTDmDABFkayUFOj9fHHa33qqaZmic+HdPvOnU05gB074E75179MNbhvv9X68svhOjn5ZK3ffjs9UsOFQLZs0frOO7Xu1g01bl59NfE1XS66CFb5smWtf21dHdyFlZXYdu9Onu/t3LlwYSYASskU/a1bUes41rjd6NX35z/Dwnn00eabFceT8nJY1127YuExNxeRAKedhoYMP/4IC3vHDsQjn3wyomuuvRaLoxdeCGvtt99Q9/uMMxLTBECILV27Ijt0/XoseD/3HKKObr01cT01p03Dz8MOa93rvF6E22Zl4W42IwPf2bq65Fhk7N4di7tJRHILebt2reuIrXXrY1ZXrsRt4G+/IdTrpJNa9/pYUlaG7L8xY3BhZmQQLVyINlT77YdQyO7dkb05YgTCEp9+GpENnTohcmXFCrhdukUvIlRIYjIzkWn8yScIT62pQejpuHFww8UzpruwEN/bigqEsYZLcAIekQmtTQYXS7duIuStondv1DZoCU6SqauDT62uruVCRFojQ3H0aCTLvPceQgqThTVrMLbzz0dYIBHuFk48kWjKFMSJv/46Jp599oGIX3opCnYtXIjY70GDUqt/pBBdBgyAVfz777hTu/FGPPbQQ60zkCLh4ovx86STwi8OxqLd1P8SjdsdOgM8gSS3kB9wABbjWsLlMvVKMjJMH7+mrI+dO2GhPPUUFg6vvDI5viDMr7/CEv/Xv4huugmZcuefD5fPVVchsadXLyxe/vgjRHv9eilaJYQmLw+5AT//jO/MokVIMrr0UvweS5QyPUzvuy+817Drz3r9ejx4PBmyicvKYpeg2EaSW8iPPRZuAy7IEwqtGxedUgpbKAvg669RbrZ/f6yyDxwY9WFHxDff4Lz/8x+iv/2N6IMPYHF//DHWDNauxcTz0UfoeTl5MtFddyV61EIqoBTRqFEoo7tyJRKM/vQnJB7dfTeyl2PB8OHwk992W3jNjLlshd8P69fjwfWdiL6goVi6NOl0I7mFPCsLCzi33GL8Y15v4Ezd3C1Y8PMeegj+wyefhLsiyW6P6JNPsIh5yy2wyrt1w9+DBhG98goWNF96CZmfp58OsR8/PtGjFlKRjh1xt7duHe7wdu7EXeABB8ByDsel2Rrefx8/zzorvOdnZBAVFcHPXlgIYW9rGHC0+eorrFMlE6FCWWK9tapDkNut9X77IQHC5cLfDQ2BSTZ1dQgXrK83W02NeU5lpdZ//KPWBx2EbM1kwudDFuZVVyELrn17JPcMG4ZQskWLAp8/bx7as82dm5jxCumL14sQ3CuuwHdsxAitH3wweo2y774b4YjJdg22hh07kFm7ZUtCDk8pGX5IBL/Y228j2WXaNFjadjusc7a4s7KMtc4/7XZsv/yCiI5OneBW6dMnsefj9cKv/Z//wE9fWopwweeeQ5nYZ57BnUJpKeqotGtnyma+8QaSgmbNQpF7QYgmdjsqMD75JPzA994LF8yBB8IlM21aZNEaEyfiZ9++URluQpg2DTX94xEW3RpCqXust1ZZ5Jzmvm4dLPPrrjPJAVar3OfD8+rrzeMzZiDN/pVXWjPpRZf6eiTsTJqEfo0FBUix//vf0bfx/vu1btdO6/ffR0f7khKtJ09GXY1Nm5BOv3Gj1o8/rnXXrujbKQjxxO3Wes4crS+8EN/Pww/HHXJbrNIvv4RVnop3lGVluGNesyZhQ6CUbb5srVeyZYvW552ndadOEMCm6oM4nSgANWCA1kuXhn+sSHG74SZ56SXUPRkzRuu8PNyi3nCD1u+8g+bKWuMW7eGH8cWYMQNNpfv313r2bAg4b7//jgzXffbReu3a+J2LIISioUHr997T+i9/gQEybJjWN90EYyXcmkIHHKD1Aw/EdpzRprwcBtjkyQkdRlNCnho9O3mBkxc7lixBfeZFi5CNeeKJWBV3OIhWr8aCyqBBSI7Jz4/JOVBFBcaxeDHcN4sXI4qkRw+s0g8bhgWRUaMa1zHx+RBKOGkS0YQJuJX905+wsNmhAxYz+Xm33orwrblzsW9BSBa8XnTImjsXNfrXr0fE1YknwvWXZCF6baauDtnVo0YhhyOBocpN9exMDSEnMv5vfhMzMiCks2bhi7RyJUIKly1DzPUVV8Af3pZGsFrjwysrQzLFxo3Y1q1Dos6aNYhdHzIEgs3CPWQIYnZb4rXXIOCHHYYEnilTkF26axfCs/bbD3Hw11yDvx9/HPtPplh3QQhm61ZkE8+di3DZPn0ggIcfju96u3bRO5bWJmKNw41jwaJFiAwbNgzrWAm+BlNfyIkCPzgrfj+avr74IkKoqqthHWzahBCm3r0hsA6H6QaUmYk+mg0NRJWVZquqwk/uwtO9O7ri9O2LrV8/bB07tu1DnTkTceB5efhyTJ6MMRLh2EphErn2Wnzx77sP8b7JEkMrCOHg8SBPY/58VGf8/nskqx1+OLbRo9uevBaqZSInAkaL6mqTPX3//QgySAJDqikhT622L6HeyLo6FIbatg2B+na76Trv92OVfcMGCGFNDZ7n8WBzu03HneJiCKrbDSFv3x5fDu5UP2hQ5HHnr76KO4WMDEw8Y8YY1099vWk7d845sGDuvx9uGSlyJaQamZlGtIkgvIsXQ9TffJPouutQmG70aETFDB0Kw6alMhla49oNzvD0eHB9Riq2S5YgYerFF1HWYOlSaEGSk1oWeTCbN8OvPHQo0u3tdgh1sPVaXw9BLCuDwHMWqN+P9Pd+/fAl8PnwZSsowOzudkPI6+rwnO7d2z7WRx8l+uc/MSG8/TbuEnbtQiKGzwcX0MaNaJh8001wqwhCuqI1Mkm//hprTL/8giQ4h8OI+tCh2Pr1My5LtsaDrW+/v21WeX09xPqzzyDglZVYdzv/fDQrTzLSwyK38v33yNK87joIpFKNm78yNhsEmz9s6+M2Gz5MhwOzOi+qbt9uyn+63RDcE05ofQMGreEPnz6d6O9/R3Ypj6G0FIubRHC5TJhA9Pzz6JEpCOmMUljTsjaO0Rp30Czqc+aYLNOCAvjcrX1rucdtTg5ySbiJeW6u6ZtbVWU2dp1u2GAmj3Xr4LocNQrG1uGHJ08GaStITSF/7TVYrM89B4ucycgwqfnWD8Pnw4cb6rZLWzrbs/+8thYiXlho/i4qQlTKiBHhf9DbtiHpZ+FCjPnss0M/7557cEfxySewRARhb0QpCHT37nBrMH4/DKsNG7Bt3Ii78R9/RNmK+nqzOZ3mp82G69a6FRdj/8cfj2qQAwdiEkhxUkvI/X6i229HvZFPP8VtlxWbjaikBI0X7Hb87fFAxIuK4MrgKmpEprYxN5Gw21Hf5McfzcKq04nHO3aEoNfVtWyVaw3hvuoqWPMLFmDGD8blQmGs337DwlCyZYsJQjJgs8H67tIF0V3sJ7eSmZkUi5GJInWE3Lqo+cMPTS+K5ObCMq+vh/AXFWHG5dl+0yb8j0OWuncPXEzs1An+68WLIeJFRTgWL3S2tKawbRuiUn79FX/PmRNaxMvL4Rpq1w4NIsIJWxQEwfTCbSqKbS8kNZxBmzfDd5WfD0u8pZVthwMCXFKCxU3+oHNz4Q/r1QvJNfvu29i6Vgphhr164bare3fsz+WC4DeVYKQ1VrqHDYPvu7YWiydHHNH4uatXw7IYORL1VETEBaH1xDJ+PMVIfot86VJkil11FXxakX5wNlvLwpmXhxrgXMpTa4j44MGh/eMbNsBFsmMH0YwZCDF8+OFAPx/zxRcIL7z7bhT7FwRBiJDkFvJvvkGz4KlTEQ4UT7p1Q/xobS3Eu7AwMOKFCK6bxx8nuvNOVC68+GKiI49EFM155zXe53//i/jxV19FxpsgCEIUSF4hnz0bwvjSS4kr2ZqdjS0Uy5ej16dSKDTfsyfE+bTTkJVpxe0muuEGog8/REPcQYNiPnRB2KvZy/znyekj/+9/IZKzZydf3W2nE4WsDj8ciQMLFiBh4dxz8fPeewOfv3kz/OSbNiEaRkRcEGKH3tP60bolIOkx3iSfkD/yCGocfP45FgOTiffeg598zRokE1x1Fdwu//43BP655wJ96PPnEx18MKz0WbMQwyoIQuzwemGFc7JfU71704zkca1ojcSYF15APYZevRI9IsP69UhAWr0aHXys/u0PPoD756efAuPT77sPmWIvvyz+cEGIB81Z3tbEvzQkOYRca9QXmTMHropkqWPscqHF3MMPw8f95puBWWAbNhBdcglqp5SW4rFt24guuAB+8YULI6vPIgiCEAaJd61ojXop8+fDnZIsIv7RR6gvvnAhtokTA0Xc5ULK/Y03olIhEVLsub/hp5+KiAtCPGnO4k5ja5woQotcKfUgEZ1KRG4iWktEF2utK1u1k3//G66U+fNNXe5Esnkz0fXXo6D8o4+GjgUnQjOITp1gqW/bhjuKTz6BK+Woo+I7ZkEQQEZG6FrlaU6kFvnHRLS/1nooEa0ioptb9eqpU9EZ/sMPEy/iHg/EefhwZHQuXdq0iFdUwN1y//14zf77Q9SXLRMRF4REohSE227HxoX00pyIpiqt9UeWP78jojPDfvFzz8Hi/fJL419OBFojGuXGG1Em89tvkbrfHMuWoQDX0UejL+c336A9myAIiWcvTN2P5j3HJUT0eljPrKgwIYaJbCj8ww/IwqyoIJo2DaUtw/kCHHoo7iK49ZsgCMkLN6PQ2ljraUaLQq6U+oSIOof41y1a63f3POcWIvIS0SvN7Gc8EY0nIuppsyFcL1FW7Pr1WLxcsIDorruILrqodR+uzUZ03HExG54gCFHC50NfXrbSXS5cv01lbKcoEbd6U0pdSERXENHRWmtnOK8ZMWCAXrhiRUTHbRMVFWh2/PzzSKP/xz+k8qAgpCtao2Q1JwYxXi+EPAUt86ZavUW02KmUOoGI/kVEp4Ur4kTUdCnYWOFyocVa//5owPzbb4iWEREXhPSlqXorNptpKpMmROojf4yIsojoY4U36zut9RURjypaaI2omJtvJhowACGOgwcnelSCIMQDpUJne6ZhlmekUSvJudLn9yMS5e678aE9/TQiTARB2HvgUESfz7hRWNjTLLY8vc7G70fHnbvvRt2Tf/+b6NRTU7IrtiAIUcDhQI4IR63wQqdY5EmIz0f0+utEkyahddu99xKddFLafViCILQS7u/JBe3SVBNSW8i9XnTbmTwZSUUPP0x07LFp+2EJgtBG0lwTUlPI3W6Ujr3nHnTmmT6daOzYtP+wBEEQQpFaQr59O9FTT2EbNAjx4GPGJHpUgiCkIlqbjROGUtQYTP5VQK2RSn/BBQgh3LKFaN48oo8/FhEXBKFtaI3gCBZxrbHWlqJt4ZLXIq+sJHrlFXTkqa4m+vvfUQ+lXbtEj0wQhHSBLXC2xlM0xjy5hLy+nuizz4hmziR6910UsZoyBaVhJYRQEIRoESzYbIlziGKKkXgh37QJfS8/+IDoiy/QYee009BirWPHRI9OEIR0hcXc7zfWuNVnnkIkRsh370b1wTlzIOQnnkj0l78QvfgiUUlJQoYkCMJeBNdbsYq4UsYaTzExT4yQV1YiZfbxx4lGjky7dFlBEFIAFvM0iFpJjIL27Ys0ekEQhEShVEqWsg1F6nn1BUEQoklwyGGKuVWIkmGxUxAEIVGwYFtrl0vUiiAIQoqRwr5xJvWmHkEQBCEAEXJBEIQUR4RcEAQhxREhFwRBSHFEyAVBEFIcEXJBEIQUR8IPBUEQmsNaGTFJQxXFIhcEQWgKroZI1Dh5KIkQIRcEQWiKUOn6VnFPEkTIBUEQWoO4VgRBEFKcJCyqJUIuCILQFNx0IvixJEOEXBAEoSlCVUNMVyFXSv1TKaWVUh2isT9BEISkIsk7CEUs5EqpHkR0LBH9HvlwBEEQhNYSDYv8ISK6kYiSKx5HEARhLyEiIVdKnUZEW7TWv0RpPIIgCEIraTFFXyn1CRF1DvGvW4hoIhEdF86BlFLjiWg8EVHPnj1bMURBEIQkRWsiv98siCbIh650GzOUlFJDiOhTInLueag7EZUR0cFa623NvXbEiBF64cKFbTquIAhCUuDz4ac1RNFmi6mYK6UWaa1HBD/e5qJZWuslRNTRcoANRDRCa72rrfsUBEFICYLrr/BPv5/Ibo/7cCSOXBAEobX4/UkVihi1MrZa697R2pcgCEJSw+6UJBFzscgFQRBaSygB17pxFmickMYSgiAIrYVT9/1+8xiLeLD/PA6IkAuCILQFpQIXNoP95tawxBgjrhVBEIRICeUvD1U5MUaIkAuCIKQ4IuSCIAgpjgi5IAhCpIRyo8QxPFGEXBAEIRoER63EMRRRolYEQRCiRYKaT4hFLgiCkOKIkAuCIKQ4IuSCIAgpjgi5IAhCiiNCLgiCEA+0RjOKGGR7StSKIAhCLOF2cESIaOHfo9iAQixyQRCEWGIVcevPKFrmIuSCIAixJlRBLWsJ3AgRIRcEQUhxRMgFQRBiic3W2I0S5VrlstgpCIIQS0J1E7Lbo5rKL0IuCIIQa4K7CUUZca0IgiCkOCLkgiAIKY4IuSAIQoojQi4IgpDiiJALgiCkOCLkgiAIKY7SMajE1eJBldpJRBvDfHoHItoVw+HEk3Q5FzmP5CJdzoMofc4lVufRS2tdGvxgQoS8NSilFmqtRyR6HNEgXc5FziO5SJfzIEqfc4n3eYhrRRAEIcURIRcEQUhxUkHIn070AKJIupyLnEdykS7nQZQ+5xLX80h6H7kgCILQPKlgkQuCIAjNkLRCrpQ6Sym1VCnlV0qNsDzeWylVr5RavGebnshxtkRT57HnfzcrpdYopVYqpY5P1BjbglLqDqXUFsvncFKix9QalFIn7Hnf1yilbkr0eNqKUmqDUmrJns9gYaLH0xqUUjOUUjuUUr9ZHmunlPpYKbV6z8+SRI4xHJo4j7heH0kr5ET0GxH9kYgWhPjfWq318D3bFXEeV2sJeR5KqUFEdC4RDSaiE4joCaVU7OpcxoaHLJ/DnEQPJlz2vM+PE9GJRDSIiM7b83mkKkfu+QxSLWzvBcJ338pNRPSp1npfIvp0z9/JzgvU+DyI4nh9JK2Qa62Xa61XJnockdLMeZxORP/TWru01uuJaA0RHRzf0e21HExEa7TW67TWbiL6H+HzEOKI1noBEe0Oevh0Ivrvnt//S0Tj4jqoNtDEecSVpBXyFuijlPpZKfWFUurwRA+mjXQjok2WvzfveSyVmKCU+nXPrWXS3wJbSIf3ntFE9JFSapFSanyiBxMFOmmttxIR7fnZMcHjiYS4XR8JFXKl1CdKqd9CbM1ZR1uJqKfW+gAiuoGIXlVKFcZnxKFp43mE6vOUVCFELZzXk0S0DxENJ3wmUxM62NaR9O99KzhMa30gwU10lVJqTKIHJBBRnK+PhLZ601of04bXuIjItef3RUqptUS0HxElbKGnLedBsAJ7WP7uTkRl0RlRdAj3vJRSzxDR7BgPJ5ok/XsfLlrrsj0/dyilZhHcRqHWlVKF7UqpLlrrrUqpLkS0I9EDagta6+38ezyuj5RzrSilSnlRUCnVl4j2JaJ1iR1Vm3iPiM5VSmUppfoQzuOHBI8pbPZcZMwZhEXdVOFHItpXKdVHKeUgLDq/l+AxtRqlVJ5SqoB/J6LjKLU+h1C8R0QX7vn9QiJ6N4FjaTPxvj6StvmyUuoMInqUiEqJ6AOl1GKt9fFENIaI7lJKeYnIR0RXaK0TutDQHE2dh9Z6qVJqJhEtIyIvEV2ltfYlcqyt5AGl1HCCS2IDEf0tscMJH621Vyk1gYg+JCI7Ec3QWi9N8LDaQicimqXQjT2DiF7VWs9L7JDCRyn1GhGNJaIOSqnNRHQ7Ed1HRDOVUpcS0e9EdFbiRhgeTZzH2HheH5LZKQiCkOKknGtFEARBCESEXBAEIcURIRcEQUhxRMgFQRBSHBFyQRCEFEeEXBAEIcURIRcEQUhxRMgFQRBSnP8H9M4p+I5ujiwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm=adaptative_imp_sampling(5, 5, 200)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that we are able to retrieve the banana shape of the original density."
   ]
  }
 ],
 "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}