Information_Theory.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Information Theory 信息论"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Name: [Your name]\n",
    "\n",
    "本次作业的目的是检查你是否了解了自信息, 信息熵和KL散度的计算, 并且学会使用. 你需要补充的代码由###来代替."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Self-information 自信息"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def self_information(p):\n",
    "    \"\"\"\n",
    "    Function: Calculate the self-information of event\n",
    "    Input:\n",
    "              p:      The probability of event p(x), type: float\n",
    "    Output:   \n",
    "              return: The self-information of event\n",
    "    \"\"\"\n",
    "    if p>1 or p<0:\n",
    "        print(\"Error: Your input is not a probability of event!\")\n",
    "        return(0)  \n",
    "    \n",
    "    # Your code\n",
    "    # Here you should calculate the self-information of event.\n",
    "    return ###"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IJOOS1Duq+lGIIhtxFxLnaohdrxWxxAThsQtOYvCJdXnw8yW8+cNav0MyxpgC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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f90550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# As the probability of event changes, how does the self-information change\n",
    "I = np.zeros(10)\n",
    "for i in range(0, 10):\n",
    "    p = 0.1*i+0.1\n",
    "    I[i] = self_information(p)\n",
    "plt.plot(np.arange(0.1, 1.1, 0.1), I)\n",
    "plt.title(\"As the probability changes, how does the self-information change\")\n",
    "plt.xlabel(\"Probability\", fontsize=20)\n",
    "plt.ylabel(\"Self-information\", fontsize=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Entopy 信息熵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def entropy(P):\n",
    "    \"\"\"\n",
    "    Function: Calculate the entopy of random variable\n",
    "    Input:\n",
    "              P:      The probability mass function(pmf) of random variable P, type: list or numpy.ndarray\n",
    "    Output:   \n",
    "              return: The entopy of random variable\n",
    "    \"\"\"\n",
    "    P = np.array(P)\n",
    "    \n",
    "    # Determine whether the input is a probability distribution\n",
    "    if P.sum()!=1 or P.max()>1 or P.min()<0:\n",
    "        print(\"Error: Your input is not a pmf!\")\n",
    "        return(0)  \n",
    "    \n",
    "    # Your code\n",
    "    # Here, you should calculate the entopy of random variable\n",
    "    return ###"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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D23Nu3zb83/urSd99JOhw6oxIEkkK8C+gJfAwsFnSK5LOq9TITLX584dr2Lz7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\nnD5taNu0HlPmpnNB/7pz+X4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qGuIKKfcx8DZwZTTEBYwC3qqO/aqccTUHVgDJ/vs20RBX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\n4kBiZmZZHEjMzCyLA4mZmWVxIDEzsyx3kGT8RBzFZPEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x80f6908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "If the coin is normal, the entopy is 1.00\n",
      "If the coin is unnormal, the entopy is 0.08\n"
     ]
    }
   ],
   "source": [
    "# As the probability changes, how does the entropy change\n",
    "p_entropy = np.zeros(9)\n",
    "for i in range(1, 10):\n",
    "    p = 0.1*i\n",
    "    p_entropy[i-1] = entropy(np.array( [p, 1-p] ))\n",
    "plt.plot(np.arange(0.1, 1, 0.1), p_entropy)\n",
    "plt.title(\"As the probability changes, how does the entropy change\")\n",
    "plt.xlabel(\"Probability of Heads\", fontsize=20)\n",
    "plt.ylabel(\"Entropy\", fontsize=20)\n",
    "plt.show()\n",
    "\n",
    "# This is the coin example\n",
    "coin_normal_p = np.array([0.5, 0.5])\n",
    "coin_normal_entopy = entropy(coin_normal_p)\n",
    "print(\"If the coin is normal, the entopy is %.2f\" % (coin_normal_entopy))\n",
    "\n",
    "coin_unnormal_p = np.array([0.01, 0.99])\n",
    "coin_unnormal_entopy = entropy(coin_unnormal_p)\n",
    "print(\"If the coin is unnormal, the entopy is %.2f\" % (coin_unnormal_entopy))\n",
    "\n",
    "#you code(optional)\n",
    "# If you think of other examples, you can be supplemented\n",
    "###"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Kullback–Leibler Divergence KL散度"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def KL_divergence(P, Q):\n",
    "    \"\"\"\n",
    "    Function: Calculate the KL Divergence between two probability distributions P and Q.\n",
    "    Input:\n",
    "              P:      The pmf of random variable P, type: list or numpy.ndarray\n",
    "              Q:      The approximate distribution of P, type: list or numpy.ndarray\n",
    "    Output:   \n",
    "              return: The KL Divergence between two probability distributions\n",
    "    \"\"\"\n",
    "    P = np.array(P)\n",
    "    Q = np.array(Q)\n",
    "    \n",
    "    # Determine whether the P and Q are the probability distribution.\n",
    "    if P.sum()!=1 or P.max()>1 or P.min()<0:\n",
    "        print(\"Error: The P is not a pmf!\")\n",
    "        return(0)\n",
    "    if Q.sum()!=1 or Q.max()>1 or Q.min()<0:\n",
    "        print(\"Error: The Q is not a pmf!\")\n",
    "        return(0)\n",
    "    \n",
    "    # Your code\n",
    "    # Here, you should calculate the KL Divergence between two probability distributions P and Q.\n",
    "    return ###"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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k907YPifJxQM693VJDugv05JmKskxSW7o3r6dZFfP9sF7ecy1SY5IsjDJ9+Z65vk0p1/n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\nuyQ16P8A9+IWHF4bqDsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x8249320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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pkjR5/EunkiRJUsMM7JIkSVLDDOySJElSwwzskiRJUsMM7JIkSVLDDOySJElS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\nLgkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x82b5400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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SAOAXQPElXAUsBX4SEZdl03oCJwEPVyNQMzNrH3KNVRURv5X0d+BrwAhSn8YC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\nh5mZ5eLEYWZmuThxtFOS7pb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      "text/plain": [
       "<matplotlib.figure.Figure at 0x82737f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This is the coin example\n",
    "coin_normal_p = np.array([0.5, 0.5])\n",
    "\n",
    "coin_unnormal_p = np.zeros([4, 2])\n",
    "coin_unnormal_p[0,:] = np.array([0.01, 0.99])\n",
    "coin_unnormal_p[1,:] = np.array([0.1, 0.9])\n",
    "coin_unnormal_p[2,:] = np.array([0.3, 0.7])\n",
    "coin_unnormal_p[3,:] = np.array([0.49, 0.51])\n",
    "\n",
    "KL_div = np.zeros(4)\n",
    "\n",
    "index = np.arange(2)\n",
    "plt.bar(index, coin_normal_p, 0.35)\n",
    "plt.ylim(0,1.1)\n",
    "plt.xticks(index, ('Heads', 'Tails'))\n",
    "plt.title(\"The normal coin.\")\n",
    "plt.show()\n",
    "\n",
    "coin_type = \"ABCD\"\n",
    "fig = plt.figure(figsize=(10.5,7))\n",
    "for i in range(4):\n",
    "    plt.subplot(2, 2, i+1)\n",
    "    plt.bar(index, coin_unnormal_p[i,:], 0.35)\n",
    "    plt.ylim(0,1.1)\n",
    "    plt.xticks(index, ('Heads', 'Tails'))\n",
    "    plt.title(\"The unnormal coin \" + coin_type[i])\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "for i in range(4):\n",
    "    KL_div[i] = KL_divergence(coin_normal_p, coin_unnormal_p[i,:])\n",
    "    name = \"The unnormal coin \" + coin_type[i]\n",
    "    plt.plot(i, KL_div[i], 'o', label=name)\n",
    "plt.title(\"The Change of KL Divergence with similarity\")\n",
    "plt.xlabel(\"The type of unnormal coin\", fontsize=20)\n",
    "plt.ylabel(\"KL Divergence\", fontsize=20)\n",
    "plt.legend(loc='best')\n",
    "plt.show()\n",
    "\n",
    "#you code(optional)\n",
    "# If you think of other examples, you can be supplemented\n",
    "####"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果你有什么疑问或者收获, 你可以在这里记录下来.\n",
    "\n",
    "###"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}