scikit/SciKit-Kernel-Density-Estimation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Kernel Density Estimation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "A density estimator takes a $D$-dimensional dataset and returns an estimate of the $D$-dimensional probability distribution from that data. GMM does this by representing the density as a weighted sum of Gaussian distributions.\n",
    "\n",
    "__Kernel density estimation__ (KDE) is process that takes the mixture-of-Gaussians idea to its logical extreme: it __uses a mixture consisting of one Gaussian component per point__, resulting in an essentially non-parametric estimator of density."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns; sns.set()\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Histograms\n",
    "\n",
    "Histograms are __1-dimensional density estimators__. They divide data into discrete bins, counts the number of points in each bin, then plot the results in an intuitive manner."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.62434536, -0.61175641, -0.52817175, -1.07296862,  0.86540763,\n",
       "       -2.3015387 ,  1.74481176, -0.7612069 ,  0.3190391 , -0.24937038])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def make_data(N, f=0.3, rseed=1):\n",
    "    rand = np.random.RandomState(rseed)\n",
    "    x = rand.randn(N)\n",
    "    x[int(f * N):] += 5\n",
    "    return x\n",
    "\n",
    "x = make_data(1000)\n",
    "x[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1000,)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A standard histogram can be created with ``plt.hist()``. The ``normed`` parameter gives us a normalized histogram. __(The bin heights instead reflect probability densities)__."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6bc48bcf98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist = plt.hist(x, bins=30, normed=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Normalization sets the total area under the histogram = 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "density, bins, patches = hist\n",
    "widths = bins[1:] - bins[:-1]\n",
    "(density * widths).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using a histogram as a density estimator can be problematic. The choice of bin size and location can lead to misleading representations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = make_data(20)\n",
    "bins = np.linspace(-5, 10, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAskAAAD8CAYAAACFHTnaAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAAFi9JREFUeJzt3X+s3XV9x/Hn9XbgxOIQL1nS1lhi955VGEwsRjZc+KFlars/NBTCgitmcaHqhmYrgwGrSipMZ5PVDFO7YNQ0FY3WpFpZiskSRYsCkrZ5b6UivVTDHaB0QekKd3+cgzt+vLfne+49936/5/T5+Ifz/X4/n+/3/fl+bz/3xfd+zzkjk5OTSJIkSfp/L6q7AEmSJKlpDMmSJElSwZAsSZIkFQzJkiRJUsGQLEmSJBUMyZIkSVJhQZVGEbES2ASMAlsyc2Ox/b3AtcBzwP8Af5mZ+9rbrgeuaW97f2bu6l/5kiRJUv91vZMcEaPAZuAyYDlwRUQsL5p9ITPPysxzgNuAT7T7LgfWAK8FVgKfau9PkiRJaqwqj1usAA5k5sHMPApsA1Z3NsjMpzsWTwFe+IaS1cC2zHw2M38EHGjvT5IkSWqsKo9bLAIOdSyPA+eXjSLiWuA64CTgoo6+9xZ9Fx3vYJOTk5MjIyMVypKkE8qsJkbnVkma0rQTY5WQPFXn3/gu68zcDGyOiCuBG4Grq/b9tYONjDAxcaRCWc03NrZwKMbiOJplWMYBwzOW+RjH2NjCWfV3bm0ex9EswzIOGJ6x1D23VnncYhxY0rG8GDh8nPbbgD+bYV9JkiSpdlVC8h5gWUQsjYiTaL0Rb0dng4hY1rH4NuC/2q93AGsi4uSIWAosA743+7IlSZKkudP1cYvMPBYR64BdtD4Cbmtm7o2IDcB9mbkDWBcRlwD/CzxF61EL2u22A/uAY8C1mfncHI1FkiRJ6otKn5OcmTuBncW6mzpef+A4fT8KfHSmBUqSJEnzzW/ckyRJkgqGZEmSJKlgSJYkSZIKhmRJkiSpYEiWJEmSCoZkSZIkqWBIliRJkgqGZEmSJKlgSJYkSZIKhmRJkiSpYEiWJEmSCoZkSZIkqWBIliRJkgqGZEmSJKlgSJYkSZIKC+ouQJIkqU5rN+6uu4RKtq6/qO4STijeSZYkSZIKhmRJkiSpYEiWJEmSCoZkSZIkqWBIliRJkgqGZEmSJKlgSJYkSZIKhmRJkiSpYEiWJEmSCpW+cS8iVgKbgFFgS2ZuLLZfB7wHOAZMAGsz88ftbc8BD7WbPpqZq/pUuyRJkjQnuobkiBgFNgOXAuPAnojYkZn7OprdD5yXmc9ExF8BtwGXt7f9IjPP6XPdkiRJ0pypcid5BXAgMw8CRMQ2YDXwq5Ccmfd0tL8XuKqfRUqSJEnzqUpIXgQc6lgeB84/TvtrgK93LL84Iu6j9SjGxsz8SrcDjo0trFDWYBiWsTiOZhmWccDwjGUQxjEINVY1LGNxHOpFL+d5WK5JneOoEpJHplg3OVXDiLgKOA94c8fqV2bm4Yg4E9gdEQ9l5sPHO+DExJEKZTXf2NjCoRiL42iWYRkHDM9Y5mMc/fhFMQznGvy5aZphGccgqHqeh+Wa1D23Vvl0i3FgScfyYuBw2SgiLgFuAFZl5rMvrM/Mw+3/HgS+BZxbpWhJkiSpLlXuJO8BlkXEUuAxYA1wZWeDiDgXuANYmZmPd6w/DXgmM5+NiFcAF9B6U58kSZLUWF3vJGfmMWAdsAvYD2zPzL0RsSEiXvg4t9uBlwJfjIgHImJHe/1rgPsi4kHgHlrPJO9DkiRJarBKn5OcmTuBncW6mzpeXzJNv28DZ82mQEmSJGm++Y17kiRJUsGQLEmSJBUMyZIkSVLBkCxJkiQVDMmSJElSwZAsSZIkFQzJkiRJUsGQLEmSJBUMyZIkSVLBkCxJkiQVDMmSJElSwZAsSZIkFQzJkiRJUsGQLEmSJBUMyZIkSVLBkCxJkiQVDMmSJElSwZAsSZIkFQzJkiRJUsGQLEmSJBUMyZIkSVLBkCxJkiQVFtRdgHSiWbtxd90lVLJ1/UV1lyBJUm28kyxJkiQVDMmSJElSodLjFhGxEtgEjAJbMnNjsf064D3AMWACWJuZP25vuxq4sd30I5l5Z59qlyRJkuZE1zvJETEKbAYuA5YDV0TE8qLZ/cB5mXk2cBdwW7vvy4GbgfOBFcDNEXFa/8qXJEmS+q/K4xYrgAOZeTAzjwLbgNWdDTLznsx8pr14L7C4/fqtwN2Z+WRmPgXcDazsT+mSJEnS3KjyuMUi4FDH8jitO8PTuQb4+nH6Lup2wLGxhRXKGgzDMhbHceKZr3M1LNdkEMYxCDVWNSxjcRzqRS/neViuSZ3jqBKSR6ZYNzlVw4i4CjgPeHOvfTtNTBypUFbzjY0tHIqxOI4T03ycq2G5JvMxjn78ohiGcw3+3DTNsIxjEFQ9z8NyTeqeW6s8bjEOLOlYXgwcLhtFxCXADcCqzHy2l76SJElSk1S5k7wHWBYRS4HHgDXAlZ0NIuJc4A5gZWY+3rFpF3Brx5v13gJcP+uqJUmSpDnU9U5yZh4D1tEKvPuB7Zm5NyI2RMSqdrPbgZcCX4yIByJiR7vvk8CHaQXtPcCG9jpJkiSpsSp9TnJm7gR2Futu6nh9yXH6bgW2zrRASZIkab75jXuSJElSwZAsSZIkFQzJkiRJUsGQLEmSJBUMyZIkSVLBkCxJkiQVDMmSJElSwZAsSZIkFQzJkiRJUsGQLEmSJBUMyZIkSVLBkCxJkiQVDMmSJElSwZAsSZIkFQzJkiRJUsGQLEmSJBUMyZIkSVLBkCxJkiQVDMmSJElSwZAsSZIkFQzJkiRJUsGQLEmSJBUMyZIkSVLBkCxJkiQVDMmSJElSYUGVRhGxEtgEjAJbMnNjsf1C4JPA2cCazLyrY9tzwEPtxUczc1U/CpckSZLmSteQHBGjwGbgUmAc2BMROzJzX0ezR4F3Ax+aYhe/yMxz+lCrJEmSNC+q3EleARzIzIMAEbENWA38KiRn5iPtbc/PQY2SJEnSvKoSkhcBhzqWx4HzezjGiyPiPuAYsDEzv9Ktw9jYwh5232zDMhbHceJZu3F33SV09bWPr667hF8ZhJ+tQaixqmEZi+NQL3o5z8NyTeocR5WQPDLFuskejvHKzDwcEWcCuyPiocx8+HgdJiaO9LD75hobWzgUY3EcaqqmXM/5+Nnqxy+Kppyv2RqWf8uOQ72qep6H5ZrUPbdW+XSLcWBJx/Ji4HDVg2fm4fZ/DwLfAs6t2leSJEmqQ5WQvAdYFhFLI+IkYA2wo8rOI+K0iDi5/foVwAV0PMssSZIkNVHXkJyZx4B1wC5gP7A9M/dGxIaIWAUQEW+IiHHgXcAdEbG33f01wH0R8SBwD61nkg3JkiRJarRKn5OcmTuBncW6mzpe76H1GEbZ79vAWbOsUZIkSZpXfuOeJEmSVDAkS5IkSQVDsiRJklQwJEuSJEkFQ7IkSZJUMCRLkiRJBUOyJEmSVDAkS5IkSQVDsiRJklQwJEuSJEkFQ7IkSZJUMCRLkiRJBUOyJEmSVDAkS5IkSQVDsiRJklQwJEuSJEkFQ7IkSZJUMCRLkiRJBUOyJEmSVDAkS5IkSQVDsiRJklQwJEuSJEkFQ7IkSZJUMCRLkiRJBUOyJEmSVFhQpVFErAQ2AaPAlszcWGy/EPgkcDawJjPv6th2NXBje/EjmXlnPwqXJEmS5krXO8kRMQpsBi4DlgNXRMTyotmjwLuBLxR9Xw7cDJwPrABujojTZl+2JEmSNHeqPG6xAjiQmQcz8yiwDVjd2SAzH8nMHwLPF33fCtydmU9m5lPA3cDKPtQtSZIkzZkqj1ssAg51LI/TujNcxVR9F3XrNDa2sOLum29YxuI41ERNup5NqmU6g1BjVcMyFsehXvRynoflmtQ5jioheWSKdZMV9z+jvhMTRyruvtnGxhYOxVgch5qqKddzPn62+vGLoinna7aG5d+y41Cvqp7nYbkmdc+tVR63GAeWdCwvBg5XPPZs+kqSJEm1qHIneQ+wLCKWAo8Ba4ArK+5/F3Brx5v13gJc33OVkiRJ0jzqeic5M48B62gF3v3A9szcGxEbImIVQES8ISLGgXcBd0TE3nbfJ4EP0wrae4AN7XWSJElSY1X6nOTM3AnsLNbd1PF6D61HKabquxXYOosaJUmSpHnlN+5JkiRJhUp3kjU31m7cXXcJlXzt46u7N5IkSXNqEHLD1vUX1V1C33gnWZIkSSoYkiVJkqSCIVmSJEkqGJIlSZKkgiFZkiRJKhiSJUmSpIIhWZIkSSoYkiVJkqSCIVmSJEkqGJIlSZKkgiFZkiRJKhiSJUmSpIIhWZIkSSoYkiVJkqSCIVmSJEkqGJIlSZKkgiFZkiRJKhiSJUmSpIIhWZIkSSosqLsANd87PvjVukuoZOv6i+ouQdI01m7cXXcJktQT7yRLkiRJBUOyJEmSVDAkS5IkSYVKzyRHxEpgEzAKbMnMjcX2k4HPAq8HngAuz8xHIuJVwH4g203vzcz39ql2SZIkaU50DckRMQpsBi4FxoE9EbEjM/d1NLsGeCozXx0Ra4CPAZe3tz2cmef0uW5JkiRpzlR53GIFcCAzD2bmUWAbsLposxq4s/36LuDiiBjpX5mSJEnS/KnyuMUi4FDH8jhw/nRtMvNYRPwcOL29bWlE3A88DdyYmf/R7YBjYwsrlDUYhmksTVflXHs9hkuTrmeTapnOINQoabD1e56pc96qEpKnuiM8WbHNT4BXZuYTEfF64CsR8drMfPp4B5yYOFKhrOYbG1s4NGMZBN3Otddj+DTles7Hz1Y/flE05XxJGl79nGfqnlurPG4xDizpWF4MHJ6uTUQsAF4GPJmZz2bmEwCZ+X3gYeD3KlcuSZIk1aDKneQ9wLKIWAo8BqwBriza7ACuBr4DvBPYnZmTETFGKyw/FxFnAsuAg32rXpIkSZoDXe8kZ+YxYB2wi9bHuW3PzL0RsSEiVrWbfQY4PSIOANcB69vrLwR+GBEP0npD33sz88l+D0KSJEnqp0qfk5yZO4GdxbqbOl7/EnjXFP2+BHxpljVKkiRJ88pv3JMkSZIKhmRJkiSpYEiWJEmSCoZkSZIkqWBIliRJkgqGZEmSJKlgSJYkSZIKhmRJkiSpUOnLRAbN2o276y5BNfC6n3gG5ZpvXX9R3SVIknrknWRJkiSpYEiWJEmSCoZkSZIkqWBIliRJkgqGZEmSJKlgSJYkSZIKhmRJkiSpYEiWJEmSCoZkSZIkqWBIliRJkgqGZEmSJKlgSJYkSZIKhmRJkiSpYEiWJEmSCoZkSZIkqWBIliRJkgoLqjSKiJXAJmAU2JKZG4vtJwOfBV4PPAFcnpmPtLddD1wDPAe8PzN39a16SZIkaQ50vZMcEaPAZuAyYDlwRUQsL5pdAzyVma8G/hn4WLvvcmAN8FpgJfCp9v4kSZKkxqryuMUK4EBmHszMo8A2YHXRZjVwZ/v1XcDFETHSXr8tM5/NzB8BB9r7kyRJkhqryuMWi4BDHcvjwPnTtcnMYxHxc+D09vp7i76Luh1wbGxhhbKm97WPlxlekjTbuXU2nJclzUSd81aVkDwyxbrJim2q9P0NExNHKpTVfGNjC4diLI6jWYZlHDA8Y5mPcfTjF8UwnGvw56ZpHEfzDMtY6p5bqzxuMQ4s6VheDByerk1ELABeBjxZsa8kSZLUKFVC8h5gWUQsjYiTaL0Rb0fRZgdwdfv1O4HdmTnZXr8mIk6OiKXAMuB7/SldkiRJmhtdQ3JmHgPWAbuA/cD2zNwbERsiYlW72WeA0yPiAHAdsL7ddy+wHdgHfAO4NjOf6/8w6nHbbbcOzLFfaF9nzaV+1tKEcc11DdPtv9dre9ttt/5Gn277nkk9verWbya1aDA5t86Oc+vs99+5zrn1xDUyOdn1EeH5Njkoz9GcccapPP7409Nun8tnabode7r2vfaDuRvHTGqZzb7m+tmmfo7nePsvx9HrtT3jjFMBfq3PdH2Pt8+Z9Cl1jqVbv5nUMl/m6bm5qd7j0Qvn1j4ce7r2zq3DNbd2HtO59cSdW/3GPUmSJKlgSJYkSZIKhmRJkiSpYEiWJEmSCoZkSZIkqTB6yy231F1D6ZZnnjladw2VTE5OcsEFfzzt9lNOOZm5Gku3Y0/Xvtd+MHfjmEkts9nXXF6PqjX0Y//lOHq9tpOTk7zpTX/0a32m63u8fc6kT6lzLN36zaSW+TLXP1vtY/zjLHfh3NqHY0/X3rl1uObWzmM6t564c6sfATeH/FrIZnEczTMsY6n7Y4oqcm5tGMfRLMMyDhiesdQ9t/q4hSRJklRo4p1kSZIkqVbeSZYkSZIKhmRJkiSpYEiWJEmSCoZkSZIkqWBIliRJkgqGZEmSJKlgSJYkSZIKC+ou4Hgi4kPA7cBYZv533fX0KiJuB94BHAUeBv4iM39Wb1XVRcRKYBMwCmzJzI01lzQjEbEE+Czwu8DzwKczc1O9Vc1cRIwC9wGPZebb665nJiLid4AtwOuASWBtZn6n3qp6FxF/A7yH1hgeovVv/Jf1VtWdc2u9nFubybm1OZoytzb2TnL7H9+lwKN11zILdwOvy8yzgf8Erq+5nsrak8Vm4DJgOXBFRCyvt6oZOwZ8MDNfA7wRuHaAxwLwAWB/3UXM0ibgG5n5+8AfMIDjiYhFwPuB8zLzdbQCz5p6q+rOubVezq2N5tzaAE2aWxsbkoF/Bv6W1v9FDKTM/GZmHmsv3gssrrOeHq0ADmTmwcw8CmwDVtdc04xk5k8y8wft10doTRqL6q1qZiJiMfA2WncKBlJEnApcCHwGIDOPDtJdwMIC4LcjYgHwEuBwzfVU4dxaL+fWBnJubZxGzK2NDMkRsYrWnzserLuWPloLfL3uInqwCDjUsTzOgE5+nSLiVcC5wHdrLmWmPkkr4DxfdyGzcCYwAfxbRNwfEVsi4pS6i+pVZj4G/BOtO7I/AX6emd+st6rjc25tBOfWZnJubYgmza21PZMcEf9O6zmm0g3A3wNvmd+KZuZ448jMr7bb3EDrz1Kfn8/aZmlkinUDe+cJICJeCnwJ+OvMfLruenoVEW8HHs/M70fEn9RdzywsAP4QeF9mfjciNgHrgX+ot6zeRMRptO4ALgV+BnwxIq7KzM/VXJdza7M5tzaMc2uzNGlurS0kZ+YlU62PiLNonZgHIwJaf0b7QUSsyMyfzmOJlUw3jhdExNXA24GLM3OQJsJxYEnH8mIG40/JU4qI36I1iX8+M79cdz0zdAGwKiL+FHgxcGpEfC4zr6q5rl6NA+OZ+cIdp7toTeSD5hLgR5k5ARARXwbeBNQakp1bG8+5tXmcW5ulMXNr4z7dIjMfAs54YTkiHqH18PYgvgN7JfB3wJsz85m66+nRHmBZRCwFHqP10PyV9ZY0MxExQusZrf2Z+Ym665mpzLye9huU2nc7PjSAkziZ+dOIOBQRkZkJXAzsq7uuGXgUeGNEvAT4Ba1x3FdvSdNzbm0M59aGcW5tnMbMrY18JnmI/AuwELg7Ih6IiH+tu6Cq2m+KWQfsovVmjO2ZubfeqmbsAuDPgYva1+GB9h0D1ed9wOcj4ofAOcCtNdfTs/bdmruAH9D6iKIXAZ+utagTh3NrMzi3No9zax+NTE4O0l+pJEmSpLnnnWRJkiSpYEiWJEmSCoZkSZIkqWBIliRJkgqGZEmSJKlgSJYkSZIKhmRJkiSp8H9saYKQsVesZgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6bc4a86438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 2, figsize=(12, 4),\n",
    "                       sharex=True, sharey=True,\n",
    "                       subplot_kw={'xlim':(-4, 9),\n",
    "                                   'ylim':(-0.02, 0.3)})\n",
    "fig.subplots_adjust(wspace=0.05)\n",
    "for i, offset in enumerate([0.0, 0.6]):\n",
    "    ax[i].hist(x, bins=bins + offset, normed=True)\n",
    "    ax[i].plot(x, np.full_like(x, -0.01), '|k',\n",
    "               markeredgewidth=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__On the left__: this is a bimodal distribution. \n",
    "\n",
    "__On the right__: this is a unimodal distribution with a long tail.\n",
    "\n",
    "This was generated from the same code. So how do you trust them?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.2, 8)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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fmaqGm4A7I+LbwPnAH084z6YZv4M4ABxidLrfScC+lZb3o1klqRCPtCWpEEtbkgqxtCWpEEtbkgqxtCWpEEtbkgqxtCWpkP8D/MBoAAHZgF8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6bc67ee128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "bins = np.arange(-3, 8)\n",
    "ax.plot(x, np.full_like(x, -0.1), '|k',\n",
    "        markeredgewidth=1)\n",
    "for count, edge in zip(*np.histogram(x, bins)):\n",
    "    for i in range(count):\n",
    "        ax.add_patch(plt.Rectangle((edge, i), 1, 1,\n",
    "                                   alpha=0.5))\n",
    "ax.set_xlim(-4, 8)\n",
    "ax.set_ylim(-0.2, 8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The height of the block stack often reflects not the actual density of points nearby, but on coincidences of how the bins align with the data points.\n",
    "\n",
    "What if, instead of stacking the blocks aligned with the *bins*, we __stack the blocks with the *points they represent*__? The blocks won't be aligned, but we can add their contributions at each location along the x-axis to find the result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6bc67d2c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_d = np.linspace(-4, 8, 2000)\n",
    "density = sum((abs(xi - x_d) < 0.5) for xi in x)\n",
    "\n",
    "plt.fill_between(x_d, density, alpha=0.5)\n",
    "plt.plot(x, np.full_like(x, -0.1), '|k', markeredgewidth=1)\n",
    "\n",
    "plt.axis([-4, 8, -0.2, 8]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result (using a __fill_between__ plot) looks messy but is a more robust reflection of the data. To smooth out the edges we could replace the blocks  with a smooth function like a Gaussian. __Let's use a standard normal curve at each point instead of a block.__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6bc69e53c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "x_d = np.linspace(-4, 8, 1000)\n",
    "density = sum(norm(xi).pdf(x_d) for xi in x)\n",
    "\n",
    "plt.fill_between(x_d, density, alpha=0.5)\n",
    "plt.plot(x, np.full_like(x, -0.1), '|k', markeredgewidth=1)\n",
    "\n",
    "plt.axis([-4, 8, -0.2, 5]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Gaussian distribution contributed at the location of each input point gives a more accurate idea of the shape of the distribution - and has less variance.\n",
    "\n",
    "The last two plots are examples of kernel density estimation in one dimension: the __first uses a so-called \"tophat\" kernel__; the __second uses a Gaussian kernel__. We'll now look at kernel density estimation in more detail."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kernel Density Estimation in Practice\n",
    "\n",
    "KDE parameters include the *kernel* (the shape of the distribution at each point) and the *kernel bandwidth* (the size of the kernel at each point).\n",
    "\n",
    "Scikit's [KDE class](http://scikit-learn.org/stable/modules/density.html) supports six kernels.\n",
    "\n",
    "KDE can be __computationally intensive__. Scikit estimator uses a tree-based algorithm and can __trade computation time for accuracy__ using the ``atol`` (absolute tolerance) and ``rtol`` (relative tolerance) parameters.\n",
    "\n",
    "The kernel bandwidth can be found using a standard cross validation tool.\n",
    "\n",
    "Replicate the above plot using Scikit's ``KernelDensity`` estimator:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.02, 0.22)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6bc9da84a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.neighbors import KernelDensity\n",
    "\n",
    "# instantiate and fit the KDE model\n",
    "kde = KernelDensity(bandwidth=1.0, kernel='gaussian')\n",
    "kde.fit(x[:, None])\n",
    "\n",
    "# score_samples returns the log of the probability density\n",
    "logprob = kde.score_samples(x_d[:, None])\n",
    "\n",
    "plt.fill_between(x_d, np.exp(logprob), alpha=0.5)\n",
    "plt.plot(x, np.full_like(x, -0.01), '|k', markeredgewidth=1)\n",
    "plt.ylim(-0.02, 0.22)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Selecting the bandwidth via cross-validation\n",
    "\n",
    "__KDE bandwidth__ is the knob that controls the bias–variance trade-off. A narrow bandwidth leads to a high-variance estimate (over-fitting), where the presence or absence of a single point makes a large difference. \n",
    "\n",
    "A wide bandwidth leads to a high-bias estimate (under-fitting) where the structure in the data is washed out by the wide kernel.\n",
    "\n",
    "There is a long history in statistics of methods to quickly estimate the best bandwidth based on rather stringent assumptions about the data: if you look up the KDE implementations in the SciPy and StatsModels packages, for example, you will see implementations based on some of these rules.\n",
    "\n",
    "SciKit's ``KernelDensity`` estimator is designed such that it can be used  with Scikit's standard grid search tools. Here we will use ``GridSearchCV`` to optimize the bandwidth.\n",
    "\n",
    "We are using a very small dataset. So let's use __leave-one-out cross-validation__, which minimizes the reduction in training set size for each trial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import GridSearchCV, LeaveOneOut"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.62434536, -0.61175641, -0.52817175, -1.07296862,  0.86540763,\n",
       "       -2.3015387 ,  6.74481176,  4.2387931 ,  5.3190391 ,  4.75062962,\n",
       "        6.46210794,  2.93985929,  4.6775828 ,  4.61594565,  6.13376944,\n",
       "        3.90010873,  4.82757179,  4.12214158,  5.04221375,  5.58281521])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "kd = KernelDensity(kernel='gaussian')\n",
    "cv = LeaveOneOut()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "bandwidths = 10 ** np.linspace(-1, 1, 100)\n",
    "#bandwidths = np.logspace(-1,1,20)\n",
    "\n",
    "#grid = GridSearchCV(kd,{'bandwidth': bandwidths},cv)\n",
    "grid = GridSearchCV(kd,{'bandwidth': bandwidths})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "grid.fit(x[:,None]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can find the choice of bandwidth which maximizes the score (which in this case defaults to the log-likelihood):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'bandwidth': 3.4304692863149193}"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grid.best_params_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: KDE on a Sphere\n",
    "\n",
    "Let's use geographic data the geographic distributions of recorded observations of two South American mammals, *Bradypus variegatus* (the Brown-throated Sloth) and *Microryzomys minutus* (the Forest Small Rice Rat). Fetch the dataset with Scikit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Downloading species data from https://ndownloader.figshare.com/files/5976075 to /home/bjpcjp/scikit_learn_data\n",
      "Downloading coverage data from https://ndownloader.figshare.com/files/5976078 to /home/bjpcjp/scikit_learn_data\n"
     ]
    }
   ],
   "source": [
    "from sklearn.datasets import fetch_species_distributions\n",
    "import numpy as np\n",
    "\n",
    "data = fetch_species_distributions()\n",
    "\n",
    "# Get matrices/arrays of species IDs and locations\n",
    "latlon = np.vstack([data.train['dd lat'],\n",
    "                    data.train['dd long']]).T\n",
    "species = np.array([d.decode('ascii').startswith('micro')\n",
    "                    for d in data.train['species']], dtype='int')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the Basemap toolkit to plot the locations of these two species on the map of South America."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/bjpcjp/miniconda3/lib/python3.6/site-packages/mpl_toolkits/basemap/__init__.py:1698: MatplotlibDeprecationWarning: The axesPatch function was deprecated in version 2.1. Use Axes.patch instead.\n",
      "  limb = ax.axesPatch\n",
      "/home/bjpcjp/miniconda3/lib/python3.6/site-packages/mpl_toolkits/basemap/__init__.py:1767: MatplotlibDeprecationWarning: The get_axis_bgcolor function was deprecated in version 2.0. Use get_facecolor instead.\n",
      "  axisbgc = ax.get_axis_bgcolor()\n",
      "/home/bjpcjp/miniconda3/lib/python3.6/site-packages/mpl_toolkits/basemap/__init__.py:3222: MatplotlibDeprecationWarning: The ishold function was deprecated in version 2.0.\n",
      "  b = ax.ishold()\n",
      "/home/bjpcjp/miniconda3/lib/python3.6/site-packages/mpl_toolkits/basemap/__init__.py:3231: MatplotlibDeprecationWarning: axes.hold is deprecated.\n",
      "    See the API Changes document (http://matplotlib.org/api/api_changes.html)\n",
      "    for more details.\n",
      "  ax.hold(b)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6bc32489e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.basemap import Basemap\n",
    "from sklearn.datasets.species_distributions import construct_grids\n",
    "\n",
    "xgrid, ygrid = construct_grids(data)\n",
    "\n",
    "# plot coastlines with basemap\n",
    "m = Basemap(projection='cyl', resolution='c',\n",
    "            llcrnrlat=ygrid.min(), urcrnrlat=ygrid.max(),\n",
    "            llcrnrlon=xgrid.min(), urcrnrlon=xgrid.max())\n",
    "\n",
    "m.drawmapboundary(fill_color='#DDEEFF')\n",
    "m.fillcontinents(color='#FFEEDD')\n",
    "m.drawcoastlines(color='gray', zorder=2)\n",
    "m.drawcountries(color='gray', zorder=2)\n",
    "\n",
    "# plot locations\n",
    "m.scatter(latlon[:, 1], latlon[:, 0], zorder=3,\n",
    "          c=species, cmap='rainbow', latlon=True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This doesn't describe density of the species, because points in the species range may overlap one another.\n",
    "\n",
    "Use KDE to show this distribution as a smooth indication of density on the map. __The coordinate system here lies on a spherical surface rather than a flat plane. Use the ``haversine`` distance metric, which represents distances on a curved surface.__\n",
    "\n",
    "There is a bit of boilerplate code here (one of the disadvantages of the Basemap toolkit) but the meaning of each code block should be clear:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/bjpcjp/miniconda3/lib/python3.6/site-packages/mpl_toolkits/basemap/__init__.py:1698: MatplotlibDeprecationWarning: The axesPatch function was deprecated in version 2.1. Use Axes.patch instead.\n",
      "  limb = ax.axesPatch\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6bc15b9f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Set up the data grid for the contour plot\n",
    "X, Y = np.meshgrid(xgrid[::5], ygrid[::5][::-1])\n",
    "land_reference = data.coverages[6][::5, ::5]\n",
    "land_mask = (land_reference > -9999).ravel()\n",
    "xy = np.vstack([Y.ravel(), X.ravel()]).T\n",
    "xy = np.radians(xy[land_mask])\n",
    "\n",
    "# Create two side-by-side plots\n",
    "fig, ax = plt.subplots(1, 2)\n",
    "fig.subplots_adjust(left=0.05, right=0.95, wspace=0.05)\n",
    "species_names = ['Bradypus Variegatus', 'Microryzomys Minutus']\n",
    "cmaps = ['Purples', 'Reds']\n",
    "\n",
    "for i, axi in enumerate(ax):\n",
    "    axi.set_title(species_names[i])\n",
    "    \n",
    "    # plot coastlines with basemap\n",
    "    m = Basemap(projection='cyl', llcrnrlat=Y.min(),\n",
    "                urcrnrlat=Y.max(), llcrnrlon=X.min(),\n",
    "                urcrnrlon=X.max(), resolution='c', ax=axi)\n",
    "    m.drawmapboundary(fill_color='#DDEEFF')\n",
    "    m.drawcoastlines()\n",
    "    m.drawcountries()\n",
    "    \n",
    "    # construct a spherical kernel density estimate of the distribution\n",
    "    kde = KernelDensity(bandwidth=0.03, metric='haversine')\n",
    "    kde.fit(np.radians(latlon[species == i]))\n",
    "\n",
    "    # evaluate only on the land: -9999 indicates ocean\n",
    "    Z = np.full(land_mask.shape[0], -9999.0)\n",
    "    Z[land_mask] = np.exp(kde.score_samples(xy))\n",
    "    Z = Z.reshape(X.shape)\n",
    "\n",
    "    # plot contours of the density\n",
    "    levels = np.linspace(0, Z.max(), 25)\n",
    "    axi.contourf(X, Y, Z, levels=levels, cmap=cmaps[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Much better."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: Not-So-Naive Bayes\n",
    "\n",
    "This example uses Bayesian generative classification with KDE, and demonstrates how to use Scikit to create a custom estimator.\n",
    "\n",
    "With a density estimation algorithm like KDE, we can remove the \"naive\" element from a Naive Bayes model and perform the same classification with a more sophisticated generative model for each class. Here's the approach:\n",
    "\n",
    "1. Split the training data by label.\n",
    "\n",
    "2. For each set, fit a KDE to obtain a generative model of the data. This allows you for any observation $x$ and label $y$ to compute a likelihood $P(x~|~y)$.\n",
    "   \n",
    "3. From the number of examples of each class in the training set, compute the *class prior*, $P(y)$.\n",
    "\n",
    "4. For an unknown point $x$, the posterior probability for each class is $P(y~|~x) \\propto P(x~|~y)P(y)$. The class which maximizes this posterior is the label assigned to the point.\n",
    "\n",
    "The algorithm is straightforward and intuitive to understand; the more difficult piece is using Scikit to apply the grid search and cross-validation tasks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.base import BaseEstimator, ClassifierMixin\n",
    "\n",
    "class KDEClassifier(BaseEstimator, ClassifierMixin):\n",
    "    \"\"\"Bayesian generative classification based on KDE\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    bandwidth (float): the kernel bandwidth within each class\n",
    "    kernel (str): the kernel name, passed to KernelDensity\n",
    "    \"\"\"\n",
    "    def __init__(self, bandwidth=1.0, kernel='gaussian'):\n",
    "        self.bandwidth = bandwidth\n",
    "        self.kernel = kernel\n",
    "        \n",
    "    def fit(self, X, y):\n",
    "        self.classes_ = np.sort(np.unique(y))\n",
    "        training_sets = [X[y == yi] for yi in self.classes_]\n",
    "        self.models_ = [KernelDensity(bandwidth=self.bandwidth,\n",
    "                                      kernel=self.kernel).fit(Xi)\n",
    "                        for Xi in training_sets]\n",
    "        self.logpriors_ = [np.log(Xi.shape[0] / X.shape[0])\n",
    "                           for Xi in training_sets]\n",
    "        return self\n",
    "        \n",
    "    def predict_proba(self, X):\n",
    "        logprobs = np.array([model.score_samples(X)\n",
    "                             for model in self.models_]).T\n",
    "        result = np.exp(logprobs + self.logpriors_)\n",
    "        return result / result.sum(1, keepdims=True)\n",
    "        \n",
    "    def predict(self, X):\n",
    "        return self.classes_[np.argmax(self.predict_proba(X), 1)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The anatomy of a custom estimator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Scikit estimators are classes. It's best for this class to inherit from ``BaseEstimator`` class and the appropriate mixin, which provides standard functionality.\n",
    "\n",
    "``BaseEstimator`` contains the logic to clone/copy an estimator for a cross-validation procedure. ``ClassifierMixin`` defines a default ``score()`` method used by such routines."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Next comes the class initialization method:__\n",
    "\n",
    "```python\n",
    "    def __init__(self, bandwidth=1.0, kernel='gaussian'):\n",
    "        self.bandwidth = bandwidth\n",
    "        self.kernel = kernel\n",
    "```\n",
    "\n",
    "This is executed when the object is instantiated with ``KDEClassifier()``.\n",
    "\n",
    "In Scikit, it is important that __initialization contains no operations other than assigning the passed values by name to ``self``.__\n",
    "\n",
    "This is due to the logic contained in ``BaseEstimator`` required for cloning and modifying estimators for cross-validation, grid search, and other functions.\n",
    "\n",
    "All arguments to ``__init__`` should be explicit. __``*args`` or ``**kwargs`` should be avoided__ - they will not be correctly handled within cross-validation routines."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__We'll handle training with ``fit()``:__\n",
    "\n",
    "```python \n",
    "    def fit(self, X, y):\n",
    "        self.classes_ = np.sort(np.unique(y))\n",
    "        training_sets = [X[y == yi] for yi in self.classes_]\n",
    "        self.models_ = [KernelDensity(bandwidth=self.bandwidth,\n",
    "                                      kernel=self.kernel).fit(Xi)\n",
    "                        for Xi in training_sets]\n",
    "        self.logpriors_ = [np.log(Xi.shape[0] / X.shape[0])\n",
    "                           for Xi in training_sets]\n",
    "        return self\n",
    "```\n",
    "\n",
    "Here we find the unique classes in the training data, train a ``KernelDensity`` model for each class, and compute the class priors based on the number of input samples.\n",
    "\n",
    "``fit()`` should always return ``self`` so that we can chain commands. For example:\n",
    "```python\n",
    "label = model.fit(X, y).predict(X)\n",
    "```\n",
    "\n",
    "Each persistent result of the fit is stored with a trailing underscore (e.g., ``self.logpriors_``).\n",
    "\n",
    "This is a SciKit convention - you can scan the members of an estimator (using IPython's tab completion) and see which members are fit to training data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Here is the prediction logic.__\n",
    "```python\n",
    "    def predict_proba(self, X):\n",
    "        logprobs = np.vstack([model.score_samples(X)\n",
    "                              for model in self.models_]).T\n",
    "        result = np.exp(logprobs + self.logpriors_)\n",
    "        return result / result.sum(1, keepdims=True)\n",
    "        \n",
    "    def predict(self, X):\n",
    "        return self.classes_[np.argmax(self.predict_proba(X), 1)]\n",
    "```\n",
    "\n",
    "Because this is a probabilistic classifier, we first implement ``predict_proba()``. It returns an array of class probabilities of shape ``[n_samples, n_classes]``.\n",
    "\n",
    "Each ``[i, j]`` of this array is the posterior probability that sample ``i`` is a member of class ``j``, computed by multiplying the likelihood by the class prior and normalizing.\n",
    "\n",
    "Finally, the ``predict()`` method uses these probabilities and simply returns the class with the largest probability."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using our custom estimator\n",
    "\n",
    "Load the digits dataset & find the cross-validation score for a range of candidate bandwidths using the ``GridSearchCV`` meta-estimator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_digits\n",
    "from sklearn.grid_search import GridSearchCV\n",
    "\n",
    "digits = load_digits()\n",
    "\n",
    "bandwidths = 10 ** np.linspace(0, 2, 100)\n",
    "grid = GridSearchCV(KDEClassifier(), {'bandwidth': bandwidths})\n",
    "grid.fit(digits.data, digits.target)\n",
    "\n",
    "scores = [val.mean_validation_score for val in grid.grid_scores_]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Plot the cross-validation score as a function of bandwidth:__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'bandwidth': 7.0548023107186433}\n",
      "accuracy = 0.9666110183639399\n"
     ]
    },
    {
     "data": {
      "image/png": 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22Qh8HKf66GNArogUqWrTsU5aWJhFIDD6L6ySktxRH5todjW08fq7+6iakcvVFy3Abz2FxixR7q8rpudx6dmzeWrVTu5/ZjM/fGgDt39yKRcvr4x3aEnPi3vMy0Qw3LfK0JlDvw78WEQ+B7wK7AGGX8/P1dzcNeqAbPbRI937+3cJheGa8+ZwqKkj3uFMeYl4f523qJTinDR+/Oi7/PCB9WzffYiPnjsbf4o1JsfDGGcfPeZrXv5r1gPRPx8qgL3RO6jqXlW9VlWXAn/vbmv1MCbj2lrXwoaagyyoyOfUeUXxDsdMYifNKuRbNy+jOD+DJ1bX8q2fvsFrG/cSHAjFOzQzTrwsEawDqkVkDs4v/euBG6N3EJFi4JCqhoA7cHoQmQnw6CvbAbjuovk2wtScUFlxNt/+7HIeX7WT1zbu5Wd/eJ/HVu2kanoOxfmZlBRkMLc8n9kzcm1pzSnIs0SgqkERuQ14Dqf76H2quklEvgu8qapPABcC3xORME7V0K1exWMOa+/qY2t9KydVFTDfZhc1McrLSuPmy4Urz57NM2/s4vX3Gti4/cjmvLTUFOaV5VNWlE1RfgbF+RkUuX9yM1PtR8ckZSuUJaG3tzXyH4+8yzXnzeGq8+bEO5yEkWz3Vzgcpqs3yMGWHhoOdbG1voWtu1vYc7Bz2P3TU/3ML89j6YISlswvtpHMo2ArlJlxU1PvNMPMr7DSgBk9n89HdkYq2TNSmTUjlzMXlgLQ1dPPwdaewT9NrT0cbO3mQHM3m2qb2VTbzK/+uJXykmyksoCTqgqpLM1hWm6GjWiOE0sESWhbfSspPh9zy/LiHYpJQFkZqVRlpFJVenQvlUNtPc6gtZqDbKtvYU9jJy+t3wM43Qzzc9KYMzOPcxbP5NT5RdbeMEEsESSZ/uAAtQ1tVJbmkJFm//xmYk3Ly+CSZRVcsqyC4ECI2n3taF0zDYe6aGrt4UBLN29vO8jb2w6Sk5nKqfOKqCrNpXJ6DsX5GYOd0rMzUslMt/t3vNgnmWRqG9oJDoSptkZiE2cBfwrzK/KPqqLcvb+d199r4I1NDax+z/kzVGogxZ01dRaFuekTFXLCskSQZKx9wEx2VaW5VJXm8omL5tFwqJu6/e3sPtBBW2cfAOGwMw7mhbfqWblhL2ctKqW6PJ/K0hzKi7NJHcPMA8nKEkGS2eYmguqKgjhHYszx+VNSKC/Oprw4m7MWHflacCDE6+818NTrh2dNdY7xMacsD6ksQCoLqJqRa0uuxsASQRIJh8PU7GmlKC/DitNmSgv4U/jgqWWce/IMahvaqTvQQd3+Dnbua2P7nlZq6lt5es0uAApy0phVmss5J8/ktAXFNj3GMCwRJJGGQ110dPezeM60eIdizLjwpzgD2OaVHa7q7O4Nsq2+lZo9LdTt72D3gQ42bm9i4/YmpuWlc/FpFVy4pIysDJtaO8ISQRI5XC1k7QMmcWWmBzhlXhGnRM2hta+pkxffqmf1uw38buV2nl6zi8uWV3DZ6ZVkW0LwdNI5M8kcbii29gGTXGYWZXPT5cIPbj2X6y6chz/FxxOra/nGT17n+TfrCE2xGRbGmyWCJLKtvoXMdD/lxdnxDsWYuMjKCPDhs2bxf754Dp+8aD7+FB8PvLCN7z/wNgdbuuMdXtxYIkgSrR297G/uZl55Pim2AI1JculpflacWcX/+sJZLJlfzPu7W/iH+9aydsv+eIcWF5YIksTmXc0ALJxlDcXGRORnp3H7x0/m8x/5AD7gvx7fxNNraplqk3GOlSWCJLG59hCArTtrzBA+n49zT57Jt25exrS8dB55ZQc//8P7SbXwjiWCJBAOh9lc20xOZiqVpTnxDseYSamiJIdvf2Y5s0pzee2dfXz/wQ00t/fGO6wJYYkgCTQc6qK5vZcPzCokxRYGMeaYCnLS+eanl7JMStha18I/3reWd7YfjHdYnrNEkAQ217rtA7OtWsiYE8lIC/ClaxZz0+UL6OkL8u8Pv8Pjq3YmdLuBJYIkEGkfWDjbGoqNiYXP5+Pi0yr4+5uXU5yfweOrdvLIKzsSNhlYIkhwoVCY93e3UFKQQUlBZrzDMWZKmTUjlztuWkZpYSbPvLGLh1duT8hkYIkgwdU2tNPdG7TSgDGjVJibzt/eeBozpmXx7J928/DLiZcMLBEkOKsWMmbsnGSwlJlFWTy7djePr9oZ75DGlSWCBLe59hA+4KQqm1/ImLEoyEnn69cvpTg/gydW1/Lsn3bHO6RxY4kggR1s7aZmTytVpbnk2uIcxoxZYW4637hhKYW56Tz0cg0vvlUf75DGhSWCBNXS0cv3H9xAcCDMBUvK4h2OMQmjpCCTr1+/hNysVH79/FYefXXqtxlYIkhA7V19/ODBDRxo7ubKc2Zx4dLyeIdkTEKZWZTNHTctY3pBJk+9vov/fnIz/cGpOyWFpwvTiMgK4G7AD9yrqncNeb0K+AVQ4O7zd6r6jJcxJbrgQIgfPrSRPQc7uXR5BR87f268QzImIc2YlsW3PrOMHz/yLm9s3k9rZx9f+9SSKTm7r2clAhHxA/cAVwALgRtEZOGQ3b4NPKSqS4HrgZ94FU+yqDvQQW1DO0uri7nhkmp8NqWEMZ7Jy0rjGzcs4ZR5RWzZ1cxz66ZmA7KXVUNnADWqukNV+4AHgauH7BMG8tzH+cBeD+NJCi3uJFnVFQWWBIyZAKkBP7dcuZC87DR+/+pO9hzsjHdII+Zl1VA5UBf1vB44c8g+3wH+KCK3A9nApSc6aWFhFoGAf9RBlZTkjvrYqaB/qzNBVlVZfsK/18nIPvPkVALc/skl/MvP1vKL55Tv334+fr83v7O9uMe8TATD/Rwd2rR+A/BzVf2BiJwN/FJEFqvqMVtdmpu7Rh1QSUkujY3toz5+KqhvcNYl9odDCf9eJ5tkuL/Msc0rzeHsRTNYs6mBXzy1iY+eM3vcrzGWe+x4CcTLqqF6oDLqeQVHV/18HngIQFXXABlAsYcxJbyW9j7AGfxijJlYN15WTUFOGk+s2sm+pqlTReRlIlgHVIvIHBFJw2kMfmLIPruBSwBE5AM4iaDRw5gSXkuH00ZgicCYiZedkcqnL1vAQCjMb17YNmXGF3iWCFQ1CNwGPAdswekdtElEvisiV7m7fQ34gohsBB4APqeqU+OTm6SaO3rJTA+Qnjb6dhRjzOidtqCExXOmsWnnIdZvnRq/az0dR+COCXhmyLY7ox5vBs71MoZk09LeS0GOTSdhTLz4fD5uvGwB/3Dvn3jwxW0snlM06X+Y2cjiBNIfHKCzJ2jVQsbE2YxpWaw4s4qmtl6eWlMb73BOyBJBAmnpsIZiYyaLK8+ezbS8dJ79025WbtgT73COyxJBAok0FBfmWiIwJt7S0/z85VWLyEwPcP+zyv3Pvk9wYHLOR2SJIIE0t0d6DFkbgTGTQXVFAXd+djmV03NYuWEv//uBt+nuDcY7rKNYIkggVjVkzORTXJDJt25exuknTaemvpX/fPw9BkKTq2RgiSCBDI4hsKohYyaV9FQ/f3HVQhbPncZ7Ow7xwAvb4h3SESwRJJDDg8msasiYycafksIXr15MeUk2L63fwwtv1p34oAliiSCBtLTbqGJjJrPM9ABfue4U8rLTeODFbWypPRTvkABLBAmluaOP3KxUAh7NemiMGbvi/Exuv/ZkUnw+fvrkZto6++IdkiWCRNLS0WulAWOmgHnl+Vx7wVxaO/v4n6e3EIrznESWCBJEd2+Q3r4BSwTGTBEfOqOKxXOm8e6OJv64Nr7tBZYIEoQ1FBsztaT4fNxy5ULys9N45JXt7GqI31oWlggSRKSh2EYVGzN15GWncctHFzIQCnPfM1viNvLYEkGCsMFkxkxNi2ZP4/xTZlJ3oINn/7Q7LjHElAhE5HoR8XTKajM2tiCNMVPXpy6eT35OGk+sro3LymaxlghuAGrdRWXKvQzIjE7z4KhiayMwZqrJykjlpsuE4ECIn/3h/QnvRRRTIlDVq3EWkEkF1onIwyJykaeRmRGxwWTGTG3LpITlUkJNfStPvV47odeOuY1AVXep6h3AdcCZwBMi8o6InO9ZdCZmLR19pPh85GVZicCYqeqmy4WivAwee20na7fsn7DrxtpGkCYiN4vIGuDfgW8DRcCXgF96GJ+JUUtHL/k5aaSk+OIdijFmlPKy0/jKJ04hI83PvU9toWZP64RcN9YSQS1wBfA3qnqGqt6vqn2qugp4wbPoTEzC4bA7qthKA8ZMdRUlOXzpmsWEQmH+45F3ONjS7fk1Y00Ey1T1RlVdM/QFVb1lnGMyI9TR3U9wIGztA8YkiMVzi7jh0mrau/r59fNbPb9erIngMyIyLfJERIpE5BsexWRGyMYQGJN4Lj6tnJOqCti4vYl3dzR5eq2Yu4+q6uB8qaraBNzoTUhmpCKNSmXF2XGOxBgzXnw+H9dfUo3PBw++uM3TUcexJoLhWiBtgNkk0Nzey/Pr6ijISeO8U2bGOxxjzDiqKs3lgiXl7Gvq4uW393h2nVgTwTYR+RsR8YlIioh8DajxLCoTsydW76QvGOKa8+eSnuqPdzjGmHF2zflzyEoP8PhrO2l1B46Ot1h/1X8Z+BXwr0AYeB24+UQHicgK4G7AD9yrqncNef2HQGRgWhYwXVULYowp6e1r6uS1jfuYWZTFuSfPiHc4xhgP5GWlcfV5c3jgxW2sXF/POR+YPu7XiCkRqOpe4GIRyXafn3AyDBHxA/cAlwH1OCOSn1DVzVHn/WrU/rcDS0cWfnJ79JUdhMJhPn7BPPwpNn+gMYnq4mXlpKf5OX9JOQO9/eN+/pi/PUQkH1gELBORD4rIB09wyBlAjaruUNU+4EHg6uPsfwPwQKzxJLtdDe28tbWReeV5LK0ujnc4xhgP+VNS+OCpZUzLy/Dk/DGVCETkU8D3gUJgDzAf2AicdpzDyoHoZXfqcaamGO78s4A5wEuxxGMY7E72odOr8PlsNLExZvRibSP4FrAMeE5Vl4rIZcC1JzhmuG+nY02pdz3wO1UdOFEghYVZBAKjbxQtKckd9bGTye5Gp3burCXlFOZ68yvBjFyi3F9m8vLiHos1EQRV9UBkTQJVfV5EvnOCY+qByqjnFcDeY+x7PXBrLIE0N3fFstuwSkpyaWyM33Jw4yUUDrN5RxPTCzIJ9vTT2DP+dYZm5BLl/jKT11juseMlkFgTQa+I+HC6kd6OM/dQyQmOWQdUi8gcnOqk6xlmEJqICE6V01HTV5jh7T3YSVdvkCXWNmCMGQexNhZ/G8gDvonT4Hsnzsyjx6SqQeA24DlgC/CQqm5yF7e5KmrXG4AHVXViV2KYwmrqnRkJqyvy4xyJMSYRnLBE4HYDna+qLwGtwKWxnlxVnwGeGbLtziHPvxPr+Yxjm5sI5lfYkAtjzNidsETgNuCecPCYmTg1e1rIzggwsygr3qEYYxJArFVDL4jIdZ5GYmLS2tFLY0sP88rzSbFuo8aYcRBrY/FtQJGIdAOdOF1Dw6o6/mOdzXFts/YBY8w4izURLPc0ChOzwfaBcksExpjxEetcQ7u8DsTEpmZPC/4UH3Nm5sU7FGNMgoh1iolGhhkVbFVDE6u3f4Dd+zuYPSOXNJty2hgzTkZTNZQBfBqw4awTqLd/gJfX72EgFGa+tQ8YY8bRaKuG7hSRl4B/Hv+QTLTu3iC/famGde/vp7t3gBSfj2ULrCBmjBk/o1puUkTmArPHNxQznKfX7OLVjXuZlpfOxadVcM7iGcwssrWJjTHjZzRtBClAKvAVr4Iyh22qPYQ/xce/3HIW6WnWLmCMGX+jaSMIAg2xTBltxqazp5/dDe1UVxZYEjDGeCbWkcW5wEFV3aWqe4AMEVnkYVwGeH9XC2Fg4azCeIdijElgsSaCXwB9Uc/73W3GQ1t2HQLgJEsExhgPxZoI/Ko62F3UXYN4VA3NJnZbdjWTnupnbpkNHjPGeCfWRNDv9hQCQETmAdZG4KHm9l72NXWxoLKAgD/WfyZjjBm5WH/V/xOwWkSedp9/GPiCNyEZgPd3NQPwAasWMsZ4LKafmqr6FPBBYD3wNvBBVX36+EeZsdjstg9YIjDGeC2mRCAiJcAuVf2Jqt4D7HK3GQ+Ew2G27Gozq+/hAAATTUlEQVQmJzOVytKceIdjjElwsVY+P8WR1UhpwJPjH44BONDczaG2Xk6qKrDFZ4wxnos1EaSralfkiap24kw+ZzywJdI+MHtanCMxxiSDmLujRFcFicj0kRxrRqa+sQOAubbmgDFmAsTaa+hHOL2G7sdZpvJm4C7PokpybV3OkI2CnLQ4R2KMSQax9hq6D6e7aB7OdBOfd7cZD7R19uEDcrJS4x2KMSYJxDr7aD6wAlgMZALLRQRVvdjL4JJVW2cfOVmp+FOs9s0Y471Yv2nuw5l1dAHwU5xRxWu9CirZtXf1kZdl1ULGmIkRayKYr6r/AHSp6gPAlRw5NfWwRGSFiKiI1IjI3x1jn0+KyGYR2SQiv4k99MQUHAjR2RMkL9sSgTFmYsSaCHrdv/tEZBrOTKQVxztARPzAPcAVwELgBhFZOGSfauAO4FxVXQT89QhiT0htnc4kr7nWPmCMmSCx9hra6iaA3wBvAC3AhhMccwZQo6o7AETkQeBqYHPUPl8A7lHVZgBVPTCC2BNSu9tjyEoExpiJEuvi9Te5D/+viKwFCoA/nOCwcqAu6nk9cOaQfRYAiMhqwA98R1WfjSWmRNXqlgjyLREYYybIiNcUUNVVMe463NwI4SHPA0A1cCFOVdNrIrJYVVuOddLCwiwCgdEv21hSkjvqYydErTOquKw0b/LHao5i/2bGa17cY14uLlMPVEY9rwD2DrPPG+6iNztFRHESw7pjnbS5uetYL51QSUkujY3toz5+IuxpaAPAFwpN+ljNkabC/WWmtrHcY8dLIF52VF8HVIvIHBFJA64Hnhiyz2PARQAiUoxTVbTDw5gmPasaMsZMNM8SgaoGgduA54AtwEOquklEvisiV7m7PQc0ichm4GXgG6ra5FVMU0F7l/UaMsZMLE/XHVbVZ4Bnhmy7M+pxGPgb94/hcPdRG1BmjJkoNofBJNPa2U9Gmp+01NE3iBtjzEhYIphk2rv6bAyBMWZCWSKYRELhMO1d/ZYIjDETyhLBJNLR3U8oHLb2AWPMhLJEMIm0RxqKrURgjJlAlggmkcM9hqzrqDFm4lgimERau6xEYIyZeJYIJpH2TnfmUWsjMMZMIEsEk0iblQiMMXFgiWASabXGYmNMHFgimETabXoJY0wcWCKYRNq6+gj4fWSm2/QSxpiJY4lgEmnrdKaX8PmGW9PHGGO8YYlgkgiHw7R19ZNr1ULGmAlmiWCS6OkboD8YsgVpjDETzhIBEBwIxTsEW4fAGBM3SZ8I3tl+kL/8/kp274/vWrORMQS52Ta9hDFmYiV9Iqjd1044DLsa4pwIImsVW4nAGDPBkj4RdPQ40zpEfpHHSyQR5FobgTFmgnm6ZvFU0NkdBKDNnednIr2zvYl1W/YztyyPXfs7ABtVbIyZeJYI3BJBexxKBL9/dQe79rez+r2GwW1WNWSMmWiWCLqdRBCZ52eidPX0s3t/O7Nn5HLBkjK0roVQKMyMoqwJjcMYY5I+EXT0OFVDXpYInly9k47uIDdcWj24bWtdK2Hg5LlFXLCknAuWlHt2fWOMOZ6kbyyOlAjaPCwRvPBWPc+/WUdTa8/gNq1rBuCkqgLPrmuMMbFI6kQQCocPtxF09xMKhcf9Gt29Qdq7nGu8tbVxcPv7u1sI+H3MLc8f92saY8xIeFo1JCIrgLsBP3Cvqt415PXPAf8H2ONu+rGq3utlTNF6eoOE3e/+cNjpSjreI3sPRpUC1usBLj+9crB9oLo8n/RUm2nUGBNfniUCEfED9wCXAfXAOhF5QlU3D9n1t6p6m1dxHE+kfSCirbNv3BPBgebuwcfb6ltp7ehlZ4MziG1BVeG4XssYY0bDy6qhM4AaVd2hqn3Ag8DVHl5vxCLtAxHtHrQTNLY4iWBBZQFhYP22g2zd3QJY+4AxZnLwMhGUA3VRz+vdbUN9XETeEZHfiUilh/EcJZIICnPTAWj1oOdQY6uTCD50hvPW1usB3t/djD/FxzxrHzDGTAJethEMt7rK0NbYJ4EHVLVXRP4K+AVw8fFOWliYRSAw+nr1kpLcwccpda0AzJqZR3N7I2FfyhGvj4dWt6H4vNMqeXZtHVt2t0A4jMyaRkWZlQgSzXjfP8YM5cU95mUiqAeif+FXAHujd1DVpqin/w3824lO2tzcNapgNmw7yMsb9vKlqxeRnuYkkn0HnInmitwSwd4D7TQ2ju/kc3sOdJCTmUpnew+nzitiW51TLTSvLHfcr2Xiq6TE/k2Nt8Zyjx0vgXhZNbQOqBaROSKSBlwPPBG9g4jMjHp6FbDFq2C21bfw7vaD1B3oGNwWqRoqc0fzjvdYglAozMGWbkoKMgFYtqBk8DWxhmJjzCThWYlAVYMichvwHE730ftUdZOIfBd4U1WfAL4sIlcBQeAQ8Dmv4ilwf/U3d/QObovMPDqzKBtgsL//eGlu72UgFKakIAOA0mlZVE3PoeFQF/PLrH3AGDM5eDqOQFWfAZ4Zsu3OqMd3AHd4GUNEYY6bCNoO9+uPlAiKCzII+H0jnm8oHA7z/Lo65pTlUV1xdH1/pMdQpEQAcOu1J9PVExysnjLGmHhLmpHFhXlHlwg63XEEOZmp5GaljXi+ob0HO3nwpRoeeWXHsK9HEsH0qERQUpDJrBnWoGiMmTySJxFESgTtUYmgux9/io/0VD95WWm0dfYRdocad/UEue/pLew/dOzG6U21znxBdQc6Bo+LFuk6Gl0iMMaYySZpEkF+ThopviMTQUd3PzmZqfh8PnKzU+kLhujtHwBg/dZGVr27j9ej1goYanPtIcCZT6gpqsopIjKq2BKBMWYyS5pE4E9JoSA348gSQU+Q7ExnsfjIgjBtboPxLncx+9bOXoYTHAih7ghh4IjeSBGNLT0E/L7BAWvGGDMZJU0iACjKz6Clo5dwODw482h2htNeHlkrONKFNJIIWjqGbzfYvqeV3v4Bphc6v/aHTwTdFOVnkpIy3Ng6Y4yZHJIqERQXZBIcCNPe3U+3O/NojlsiiEw2197ZRygUps5dQ7ilY/gSwSa3WuhDpztj5oYmgu7eIB3d/YNdR40xZrJKqkRQlOd8KTe39Q52Hc3OcBNBtvN3a1cf+5u7BtsKWo9RIti005kv6KxFM8jOCByVCIbrOmqMMZNRUiWCafluIujoHew6mp3pVA1Flwgi1UIAbV19DIRCR5yns6ef2oY25pblkZkeoHJ6Do3N3fT0HZ7WurHFaTyebonAGDPJJVUiKHa/lJvbe+k4qkRwuLF4d4Pz674gJ41wGNo6jxxxvKW2mXAYFs2eBkDl9FzCQH1j5+A+ViIwxkwVSZUIiiIlgvbDVUORNoLcrMONxZESweK5RcDRPYci3UYXzokkghzgyHYCSwTGmKkiqRJBcb7zpdzSHl01FEkEzt9tnX3samintDCTmdOy3P2PbCfYVHuIzPQAc2Y6I4SPlwiK862x2BgzuSVVIhhsI2jviaoactoIAv4UsjMC7NrfTldvkFkzcsnPcUoJLVElgkNtPTS29HBSVQH+FOfjKyvOxp/io86d1jocDtNwqIu8rFQy0z2dzskYY8YsqRJBRlqA7IwAzR19R1UNgdNO0NPn9BaaVZpLvjstRUvUILR9Tc6UE5FSAEBqIIUZRVnUH+gkFA7z+nsNHGztsTWJjTFTQlIlAnCmo25u76Gz58jGYuCIheurZuRS4CaC6FlJ97sL45S61UYRldNz6O0fYOe+Nn77Ug3pqX4+ddF8z96HMcaMl6RLBIU56XT3DtDU6nTvjHQfhcOji8EpERS4VUPRYwki8weVFh6dCAD+3+Ob6Oju5+rz5gw2ThtjzGSWdBXYkXl/6ho7CfidmUcjIvMNFeVlkJOZSjgcJjWQcsTU1ZHZSCNTS0REEsHB1h4qp+dw2ekVnr4PY4wZL8lXInATQXdvkOwMZ+bRiFx3dHFkvQCfz0d+dhqt0YmguZvsjMARbQvgjCUA8AGfWSGDDcnGGDPZJW2JAA53HY2ItBHMKj3cEFyQk872va2EQs56A40t3VSVHr2wTH52GhcsKaOkIJN5tgylMWYKSe5EkHHk219SXcymnYc4e/GMwW2R0cXtXX30BUMMhMKUTht+kNhnV5zkTdDGGOOhJEwEhxtwh1bvFOSkc+u1Jx+xbbALaUff4NiDoQ3FxhgzlSVhIoguEaQeZ09HpOdQS0fv4CpkQxuKjTFmKku6Fs3sjAABv/O2o7uOHkv0WIL9h4bvOmqMMVNZ0iUCn8/HNLdUMLRqaDiD00y093JgcDCZlQiMMYkj6RIBOKOLIdaqIbeNoLNvsOtoLMcZY8xUkZSJIFIiGNp9dDiRROBMNtd91NQSxhgz1SVnInCXrMzLOnEicNoUfOzY2+Z0HbWGYmNMgvG015CIrADuBvzAvap61zH2uw54GDhdVd/0MiaAS5dXkJedRnVlwQn3dUYXp0f1GLISgTEmsXhWIhARP3APcAWwELhBRBYOs18u8GXgT17FMlRBTjqXn15JStT0Esff//BkdFYiMMYkGi+rhs4AalR1h6r2AQ8CVw+z3z8D/xvo8TCWMYm0E4CVCIwxicfLqqFyoC7qeT1wZvQOIrIUqFTVp0Tk67GctLAwi0DAf+Idj6Gk5Oh5gk5kRkkObG0EYFF1CTlR6xYYE20095cxI+HFPeZlIhiu3iUceSAiKcAPgc+N5KTNbl/+0SgpyaWxsX3Ex6X7nbeSk5lKd2cv3UMWszcGRn9/GROrsdxjx0sgXlYN1QOVUc8rgL1Rz3OBxcBKEakFzgKeEJHlHsY0KpFBZTa1hDEmEXlZIlgHVIvIHGAPcD1wY+RFVW0FiiPPRWQl8PWJ6DU0UpE2AmsoNsYkIs9KBKoaBG4DngO2AA+p6iYR+a6IXOXVdb0we0YuM6ZlsbS6JN6hGGPMuPOFw+ET7zWJNDa2jzpgq8M1XrL7y3htjG0Ex+wvn5Qji40xxhxmicAYY5KcJQJjjElylgiMMSbJWSIwxpgkZ4nAGGOSnCUCY4xJcpYIjDEmyU25AWXGGGPGl5UIjDEmyVkiMMaYJGeJwBhjkpwlAmOMSXKWCIwxJslZIjDGmCRnicAYY5KcJQJjjElyXq5ZPOmJSDbwE6APWKmqv45zSCaBiMhc4O+BfFW9Lt7xmMQiItcAHwGmA/eo6h9He66EG1ksIvcBVwIHVHVx1PYVwN2AH7hXVe8SkZuBFlV9UkR+q6qfik/UZqoYyf0V9drvLBGYWIzy/ioEvq+qnx/tdROxaujnwIroDSLiB+4BrgAWAjeIyEKgAqhzdxuYwBjN1PVzYr+/jBmpnzPy++vb7uujlnCJQFVfBQ4N2XwGUKOqO1S1D3gQuBqox0kGkICfhRl/I7y/jBmRkdxfIuITkX8D/qCq68dy3WT58ivn8C9/cBJAOfAo8HER+U/gyXgEZhLCsPeXiBSJyH8BS0XkjviEZhLAsb6/bgcuBa4Tkb8aywWSpbHYN8y2sKp2An820cGYhHOs+6sJGNN/UGM49v31I+BH43GBZCkR1AOVUc8rgL1xisUkHru/jJc8v7+SpUSwDqgWkTnAHuB64Mb4hmQSiN1fxkue318JVyIQkQeANc5DqReRz6tqELgNeA7YAjykqpviGaeZmuz+Ml6K1/2VcOMIjDHGjEzClQiMMcaMjCUCY4xJcpYIjDEmyVkiMMaYJGeJwBhjkpwlAmOMSXKWCEzCEpGwiOR4eP4LReTNEey/XESGXfNCRGaLyEH3cYGI/O2Q11eKyJVji9iY4VkiMGaCqOqbqvrpGHYtAP72hHsZM06SZYoJk7y+LiKXA0XAt1T1EQD3l7kA6UAN8Oeq2iwiFwL/DvwJOBsIA9er6hb3uP+FM8R/D7A2chF3ROijqvqw+2v+74FpqjogIpuBa4AynAVElrvH3Ap8FdgHrIyK+R6gQEQ2AF2qeo67/QIR+Tv3PA+p6t+N4+dkkpiVCEyiC7lfpFcBPxWR6e72r6jqclU9GdgEfDPqmEXAf6nqKcBDOAt/ICIfdc+zBLgYOCnqmBeBS9zHl7jnPF1EZgK5qro1OigROQUnWZyrqufjJKqIW3FWzlsSlQQAqoAPAkuBW0SkeuQfhzFHs0RgEt3/AKiqAuuBs9ztnxGRt0TkXZwJvJZEHaOq+rb7+A1gnvv4IuC3qtqhqgORc7teBC4VkTSc2SF/ijNX/KXua0NdCDytqvvd5z+N4b08rKohVW3FmXNm3okOMCYWlghMMvEBYRE5H/gisMItEXwbyIjaryfq8QCHq1CHmxceAFXdifP/6UacScMiJYRLgJeOEctIHSsuY8bEEoFJdH8G4FajLMGp+y8AWoEmEUkH/jzGc70IfFJEst11ZIcuavQS8B3gBVWtw6nuuZzhE8HLwIejqqqiFx5vA7JExL7ozYSwRGASXa+IrAaeAv5SVQ8AfwC2A++7j2Na71VVn3LPswHny/3tIbu8iFOPH/niXwW0q2r9MOd6B/hXYLWIvIbT+Bx57RDwa+BdEXk9xvdpzKjZNNTGGJPkrERgjDFJzhKBMcYkOUsExhiT5CwRGGNMkrNEYIwxSc4SgTHGJDlLBMYYk+QsERhjTJL7/2n8zhX+w1BiAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6bc66f9128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogx(bandwidths, scores)\n",
    "plt.xlabel('bandwidth')\n",
    "plt.ylabel('accuracy')\n",
    "plt.title('KDE Model Performance')\n",
    "print(grid.best_params_)\n",
    "print('accuracy =', grid.best_score_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that this not-so-naive Bayesian classifier reaches a cross-validation accuracy of just over 96%; this is compared to around 80% for the naive Bayesian classification:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.81860038035501381"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.naive_bayes import GaussianNB\n",
    "from sklearn.cross_validation import cross_val_score\n",
    "cross_val_score(GaussianNB(), digits.data, digits.target).mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One advantage of generative classifiers is interpretability of results: for each unknown sample, we not only get a probabilistic classification, but a *full model* of the distribution of points we are comparing it to!\n",
    "\n",
    "Here are some potential improvements:\n",
    "\n",
    "- we could allow the bandwidth in each class to vary independently\n",
    "- we could optimize these bandwidths not based on their prediction score, but on the likelihood of the training data under the generative model within each class (i.e. use the scores from ``KernelDensity`` itself rather than the global prediction accuracy)"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "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": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}