04-entropia_cruzada.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Entropía cruzada"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dadas dos distribuciones de probabilidad, la entropía cruzada mide el grado de similitud entre las distribuciones"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Se basa en KL-divergence $D_{KL}(p||q)$ (Kullback-Leibler)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\huge H(p,q) = - \\sum_{i=1}^N{p_i log(q_i)} = H(p) + D_{KL}(p||q)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\large D_{KL}(p||q) = \\sum_{i}{p_i log(p_i/q_i)}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La divergencia KL es cero cuando las dos distribuciones son iguales.\n",
    "\n",
    "Cual es el valor de la entropía cruzada mínimo?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cross_entropy(P, Q):\n",
    "    \"\"\"\n",
    "    Calcula la entropía curzada entre de dos distribuciones\n",
    "    \"\"\"\n",
    "    ce = 0\n",
    "    for i, p in P.items():\n",
    "        ce = ce - p*np.log(Q[i])\n",
    "    return ce/np.log(len(P))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = {1: 0.175, 2: 0.1, 3: 0.25, 4:0.05, 5:0.125, 6: 0.1, 7:0.2}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9474818901754604"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cross_entropy(X, X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: 0.175, 2: 0.1, 3: 0.25, 4: 0.05, 5: 0.125, 6: 0.1, 7: 0.2}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dada una V.A X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(X.values())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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q8OvA1UlmgT+qqi+Ot6pLuhm4E3i2W/MG+MOqOjTGmka5FvhSd5bCW4C/rqpVccriKnINcGBuHsAa4KGqemS8JfXyO8BXuqWQk3S3U1nJkrwNuBX47XHXcjGeXilJjXPpRpIaZ9BLUuMMeklqnEEvSY0z6CWpcQa9JDXOoJekxv0/tPcXuzOPg3UAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.bar(X.keys(), X.values())\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6, 3, 3, 7, 2, 2, 1, 1, 1, 7, 3, 7, 5, 6, 1, 5, 1, 3, 2, 1, 7, 6,\n",
       "       3, 1, 1, 7, 1, 3, 7, 7, 3, 1, 7, 1, 5, 1, 2, 3, 7, 2, 7, 3, 3, 2,\n",
       "       5, 3, 6, 3, 2, 3, 5, 3, 1, 7, 3, 7, 3, 1, 7, 4, 3, 7, 7, 3, 1, 5,\n",
       "       3, 5, 1, 6, 4, 2, 5, 4, 7, 6, 5, 1, 3, 1, 3, 5, 3, 5, 3, 6, 5, 7,\n",
       "       5, 3, 2, 3, 1, 2, 1, 1, 6, 3, 6, 1])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.choice(list(X.keys()), size = 100, p = list(X.values()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def estimate_and_get_ce(X, N):\n",
    "    \"\"\"\n",
    "        Dado una distribución X y la cantidad de veces N que se realiza el muestreo de la distribución, \n",
    "        devuelve la entropía cruzada entre X y la estimación de X\n",
    "    \"\"\"\n",
    "    # Muestramos la V.A X, N veces\n",
    "    observaciones = np.random.choice(list(X.keys()), size = N, p = list(X.values()))\n",
    "    # Calculamos histograma\n",
    "    ps, _ = np.histogram(observaciones, bins=len(X), range=[1,len(X)+1])\n",
    "    # Normalizamos\n",
    "    ps = ps/len(observaciones)\n",
    "    X_ = {k:ps[i] for i,k in enumerate(X.keys())}\n",
    "    return cross_entropy(X, X_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "entropies = []\n",
    "Ns = []\n",
    "for N in range(200):\n",
    "    obs = 100 + N*100\n",
    "    Ns.append(obs)\n",
    "    entropies.append(estimate_and_get_ce(X, obs))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(20,5))\n",
    "plt.plot(Ns, entropies)\n",
    "plt.xscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: 0.175, 2: 0.1, 3: 0.25, 4: 0.05, 5: 0.125, 6: 0.1, 7: 0.2}"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9474818901754604"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cross_entropy(X, X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Intuición de la entropía Cruzada:\n",
    "\n",
    "https://www.quora.com/Whats-an-intuitive-way-to-think-of-cross-entropy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}