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    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#Kullback-Leibler-Divergence\" data-toc-modified-id=\"Kullback-Leibler-Divergence-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Kullback-Leibler Divergence</a></span></li><li><span><a href=\"#Reference\" data-toc-modified-id=\"Reference-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>Reference</a></span></li></ul></div>"
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   "source": [
    "# code for loading the format for the notebook\n",
    "import os\n",
    "\n",
    "# path : store the current path to convert back to it later\n",
    "path = os.getcwd()\n",
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  {
   "cell_type": "code",
   "execution_count": 2,
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     "text": [
      "Ethen 2018-10-13 21:20:42 \n",
      "\n",
      "CPython 3.6.4\n",
      "IPython 6.4.0\n",
      "\n",
      "numpy 1.14.1\n",
      "scipy 1.1.0\n",
      "matplotlib 2.2.2\n"
     ]
    }
   ],
   "source": [
    "os.chdir(path)\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import binom\n",
    "\n",
    "# 1. magic for inline plot\n",
    "# 2. magic to print version\n",
    "# 3. magic so that the notebook will reload external python modules\n",
    "# 4. magic to enable retina (high resolution) plots\n",
    "# https://gist.github.com/minrk/3301035\n",
    "%matplotlib inline\n",
    "%load_ext watermark\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "%config InlineBackend.figure_format='retina'\n",
    "%watermark -a 'Ethen' -d -t -v -p numpy,scipy,matplotlib"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Kullback-Leibler Divergence"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this post we're going to take a look at way of comparing two probability distributions called **Kullback-Leibler Divergence (a.k.a KL divergence)**. Very often in machine learning, we'll replace observed data or a complex distributions with a simpler, approximating distribution. KL Divergence helps us to measure just how much information we lose when we choose an approximation, thus we can even use it as our objective function to pick which approximation would work best for the problem at hand.\n",
    "\n",
    "Let's look at an example: (The example here is borrowed from the following link. [Blog: Kullback-Leibler Divergence Explained](https://www.countbayesie.com/blog/2017/5/9/kullback-leibler-divergence-explained)).\n",
    "\n",
    "Suppose we're a group of scientists visiting space and we discovered some space worms. These space worms have varying number of teeth. After a decent amount of collecting, we have come to this empirical probability distribution of the number of teeth in each worm:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 392,
       "width": 512
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ensure the probability adds up to 1\n",
    "true_data = np.array([0.02, 0.03, 0.05, 0.14, 0.16, 0.15, 0.12, 0.08, 0.1, 0.08, 0.07])\n",
    "n = true_data.shape[0]\n",
    "index = np.arange(n)\n",
    "assert sum(true_data) == 1.0\n",
    "\n",
    "# change default style figure and font size\n",
    "plt.rcParams['figure.figsize'] = 8, 6\n",
    "plt.rcParams['font.size'] = 12\n",
    "\n",
    "plt.bar(index, true_data)\n",
    "plt.xlabel('Teeth Number')\n",
    "plt.title('Probability Distribution of Space Worm Teeth')\n",
    "plt.ylabel('Probability')\n",
    "plt.xticks(index)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we need to send this information back to earth. But the problem is that sending information from space to earth is expensive. So we wish to represent this information with a minimum amount of information, perhaps just one or two parameters. One option to represent the distribution of teeth in worms is a uniform distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 392,
       "width": 512
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "uniform_data = np.full(n, 1.0 / n)\n",
    "\n",
    "# we can plot our approximated distribution against the original distribution\n",
    "width = 0.3\n",
    "plt.bar(index, true_data, width=width, label='True')\n",
    "plt.bar(index + width, uniform_data, width=width, label='Uniform')\n",
    "plt.xlabel('Teeth Number')\n",
    "plt.title('Probability Distribution of Space Worm Teeth')\n",
    "plt.ylabel('Probability')\n",
    "plt.xticks(index)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another option is to use a binomial distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p for binomial distribution: 0.49454545454545457\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([0.00055018, 0.00592134, 0.0289677 , 0.08502751, 0.16638476,\n",
       "       0.22791121, 0.22299226, 0.15584249, 0.07623949, 0.02486468,\n",
       "       0.00486561])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# we estimate the parameter of the binomial distribution\n",
    "p = true_data.dot(index) / n\n",
    "print('p for binomial distribution:', p)\n",
    "binom_data = binom.pmf(index, n, p)\n",
    "binom_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 392,
       "width": 512
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "width = 0.3\n",
    "plt.bar(index, true_data, width=width, label='True')\n",
    "plt.bar(index + width, binom_data, width=width, label='Binomial')\n",
    "plt.xlabel('Teeth Number')\n",
    "plt.title('Probability Distribution of Space Worm Teeth')\n",
    "plt.ylabel('Probability')\n",
    "plt.xticks(np.arange(n))\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comparing each of our models with our original data we can see that neither one is the perfect match, but the question now becomes, which one is better?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 392,
       "width": 512
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.bar(index - width, true_data, width=width, label='True')\n",
    "plt.bar(index, uniform_data, width=width, label='Uniform')\n",
    "plt.bar(index + width, binom_data, width=width, label='Binomial')\n",
    "plt.xlabel('Teeth Number')\n",
    "plt.title('Probability Distribution of Space Worm Teeth Number')\n",
    "plt.ylabel('Probability')\n",
    "plt.xticks(index)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given these two distributions that we are using to approximate the original distribution, we need a quantitative way to measure which one does the job better. This is where **Kullback-Leibler (KL) Divergence** comes in.\n",
    "\n",
    "KL Divergence has its origins in information theory. The primary goal of information theory is to quantify how much information is in our data. To recap, one of the most important metric in information theory is called Entropy, which we will denote as $H$. The entropy for a probability distribution is defined as:\n",
    "\n",
    "\\begin{align}\n",
    "H = -\\sum_{i=1}^N p(x_i) \\cdot \\log p(x_i)\n",
    "\\end{align}\n",
    "\n",
    "If we use $log_2$ for our calculation we can interpret entropy as, using a distribution $p$, the minimum number of bits it would take us to encode events drawn from distribution $p$. Knowing we have a way to quantify how much information is in our data, we now extend it to quantify how much information is lost when we substitute our observed distribution for a parameterized approximation.\n",
    "\n",
    "The formula for Kullback-Leibler Divergence is a slight modification of entropy. Rather than just having our probability distribution $p$ we add in our approximating distribution $q$, then we look at the difference of the log values for each:\n",
    "\n",
    "\\begin{align}\n",
    "D_{KL}(p || q) = \\sum_{i=1}^{N} p(x_i)\\cdot (\\log p(x_i) - \\log q(x_i))\n",
    "\\end{align}\n",
    "\n",
    "Essentially, what we're looking at with KL divergence is the expectation of the log difference between the probability of data in the original distribution with the approximating distribution. Because we're multiplying the difference between the two distribution with $p(x_i)$, this means that matching areas where the original distribution has a higher probability is more important than areas that has a lower probability. Again, if we think in terms of $\\log_2$, we can interpret this as, how many extra bits of information we need to encode events drawn from true distribution $p$, if using an optimal code from distribution $q$ rather than $p$.\n",
    "\n",
    "The more common way to see KL divergence written is as follows:\n",
    "\n",
    "\\begin{align}\n",
    "D_{KL}(p || q) = \\sum_{i=1}^N p(x_i) \\cdot \\log \\frac{p(x_i)}{q(x_i)}\n",
    "\\end{align}\n",
    "\n",
    "since $\\text{log}a - \\text{log}b = \\text{log}\\frac{a}{b}$.\n",
    "\n",
    "If two distributions, $p$ and $q$ perfectly match, $D_{KL}(p || q) = 0$, otherwise the lower the KL divergence value, the better we have matched the true distribution with our approximation.\n",
    "\n",
    "Side Note: If you're interested in having an understanding of the relationship between entropy, cross entropy and KL divergence, the following links are good places to start. Maybe they will clear up some of the hand-wavy explanation of these concepts ... [Youtube: A Short Introduction to Entropy, Cross-Entropy and KL-Divergence](https://www.youtube.com/watch?v=ErfnhcEV1O8) and [StackExchange: Why do we use Kullback-Leibler divergence rather than cross entropy in the t-SNE objective function?](https://stats.stackexchange.com/questions/265966/why-do-we-use-kullback-leibler-divergence-rather-than-cross-entropy-in-the-t-sne/265989)\n",
    "\n",
    "Given these information, we can go ahead and calculate the KL divergence for our two approximating distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "KL(True||Uniform):  0.13667971094966938\n",
      "KL(True||Binomial):  0.32819435311402045\n"
     ]
    }
   ],
   "source": [
    "# both function are equivalent ways of computing KL-divergence\n",
    "# one uses for loop and the other uses vectorization\n",
    "def compute_kl_divergence(p_probs, q_probs):\n",
    "    \"\"\"\"KL (p || q)\"\"\"\n",
    "    kl_div = 0.0\n",
    "    for p, q in zip(p_probs, q_probs):\n",
    "        kl_div += p * np.log(p / q)\n",
    "\n",
    "    return kl_div\n",
    "\n",
    "\n",
    "def compute_kl_divergence(p_probs, q_probs):\n",
    "    \"\"\"\"KL (p || q)\"\"\"\n",
    "    kl_div = p_probs * np.log(p_probs / q_probs)\n",
    "    return np.sum(kl_div)\n",
    "\n",
    "\n",
    "print('KL(True||Uniform): ', compute_kl_divergence(true_data, uniform_data))\n",
    "print('KL(True||Binomial): ', compute_kl_divergence(true_data, binom_data))"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see the information lost by using the Binomial approximation is greater than using the uniform approximation. If we have to choose one to represent our observations, we're better off sticking with the Uniform approximation.\n",
    "\n",
    "To close this discussion, we used KL-divergence to calculate which our approximate distribution more closely reflects our true distribution. One caveat to note is that it may be tempting to think of KL-divergence as a way of measuring distance, however, whenever we talk about KL-divergence, we do not categorized it as a distance metric due to the fact that it is asymmetric. In other words, $D_{KL}(p || q) \\neq D_{KL}(q || p)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reference"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- [Blog: Kullback-Leibler Divergence Explained](https://www.countbayesie.com/blog/2017/5/9/kullback-leibler-divergence-explained)\n",
    "- [Youtube: A Short Introduction to Entropy, Cross-Entropy and KL-Divergence](https://www.youtube.com/watch?v=ErfnhcEV1O8)\n",
    "- [StackExchange: Why do we use Kullback-Leibler divergence rather than cross entropy in the t-SNE objective function?](https://stats.stackexchange.com/questions/265966/why-do-we-use-kullback-leibler-divergence-rather-than-cross-entropy-in-the-t-sne/265989)"
   ]
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