Pomegranate.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pomegranate library\n",
    "\n",
    "[`pomegranate` is a Python package](https://pomegranate.readthedocs.io/en/latest/index.html) that implements fast and flexible probabilistic models ranging from individual probability distributions to compositional models such as [Bayesian networks](https://en.wikipedia.org/wiki/Bayesian_network) and [Hidden Markov models](https://en.wikipedia.org/wiki/Hidden_Markov_model). \n",
    "\n",
    "The core philosophy behind pomegranate is that **all probabilistic models can be viewed as a probability distribution in that they all yield probability estimates for samples and can be updated given samples and their associated weights**. The primary consequence of this view is that the components that are implemented in pomegranate can be stacked more flexibly than other packages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pomegranate import *\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import matplotlib as mpl\n",
    "mpl.rcParams['figure.dpi']= 150"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## Probability distributions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Initialization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "n1 = NormalDistribution(5, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Random samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4.63182744,  6.36621905,  1.79253477,  2.47307143,  4.9550475 ,\n",
       "       12.03512287,  1.45765111,  3.75971927,  5.63179653,  5.98264793])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n1.sample(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What's the probability of a sample data?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.17603266338221998"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n1.probability(6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.737085713764219"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n1.log_probability(6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.19947114, 0.17603266, 0.00876415, 0.00043634])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n1.probability([5,6,0,-2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fitting with an array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[5.0, 2.0]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n1.parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.random.normal(3.5,2.0,1000)+np.random.random(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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": [
    "plt.hist(a,bins=20, edgecolor='k')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "n1.fit(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[3.8909056080889504, 2.0772587381572114]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n1.parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Creating the distribution from the sample data directly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "n2 = NormalDistribution.from_samples(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{\n",
      "    \"class\" : \"Distribution\",\n",
      "    \"name\" : \"NormalDistribution\",\n",
      "    \"parameters\" : [\n",
      "        3.8909056080889504,\n",
      "        2.0772587381572114\n",
      "    ],\n",
      "    \"frozen\" : false\n",
      "}\n"
     ]
    }
   ],
   "source": [
    "print(n2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting (histogram) is natively supported on the distribution class with the `plot()` method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "beta = BetaDistribution(2,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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": [
    "beta.plot(500,\n",
    "          bins=20,\n",
    "          edgecolor='k',\n",
    "          color='orange')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discrete distribution\n",
    "\n",
    "Instead of passing parameters as floats, you instead pass in a dictionary where keys can be any objects and values are the probability of them occurring."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "discrete = DiscreteDistribution({'Harry':0.25, 'Ron':0.2, 'Hermione':0.35, 'Draco':0.2})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.25"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "discrete.probability('Harry')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "discrete.probability('Hagrid')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Ron', 'Draco', 'Ron', 'Ron', 'Draco', 'Hermione', 'Draco',\n",
       "       'Draco', 'Harry', 'Hermione'], dtype='<U8')"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "discrete.sample(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fitting a discrete distribution is easy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# A DNA sequence\n",
    "dna_data = 'ACGATACACTGAATGACAGCAGTCACTGACAGTAGTACGAGTAGTAGCAGAGAGTAATAAAGAATTAATATATGACACTACGAAAAAAATGCATCG'\n",
    "dna = list(dna_data)\n",
    "# Starting with a equi-probability distribution of the 4 nucleic acids\n",
    "d = DiscreteDistribution({'A':0.25,'T':0.25,'G':0.25,'C':0.25})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "d.fit(dna)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "From the given DNA sequence, the probabilities are [{'A': 0.4375, 'T': 0.19791666666666666, 'G': 0.20833333333333334, 'C': 0.15625}]\n"
     ]
    }
   ],
   "source": [
    "print (\"From the given DNA sequence, the probabilities are\", d.parameters)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A simple DNA sequence matching application"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.4375    , 0.19791667, 0.20833333, 0.15625   ])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dna_params = np.array(list(d.parameters[0].values()))\n",
    "dna_params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gen_seq(length=100):\n",
    "    from random import choices\n",
    "    seq = ''.join(choices(['A','T','G','C'],k=length))\n",
    "    return seq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "dna_seq = []\n",
    "for _ in range(5):\n",
    "    dna_seq.append(gen_seq(96))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean-square distance (of nucleic acid proportions) between\n",
      " ACGATACACTGAATGACAGCAGTCACTGACAGTAGTACGAGTAGTAGCAGAGAGTAATAAAGAATTAATATATGACACTACGAAAAAAATGCATCG\n",
      " and\n",
      " GCGAAGGCCGACGCCGACCTCCTCTGACTGTCGACCGTGGTAGGTGATTGCTGCTTCGGCATTTTCCATAGGCTATACGTTGCAGGCCCGCGCAGG\n",
      " is 0.335\n",
      "----------------------------------------------------------------------------------------------------\n",
      "The mean-square distance (of nucleic acid proportions) between\n",
      " ACGATACACTGAATGACAGCAGTCACTGACAGTAGTACGAGTAGTAGCAGAGAGTAATAAAGAATTAATATATGACACTACGAAAAAAATGCATCG\n",
      " and\n",
      " CTGAGGCATCAGAACACAGCATATGGGCTGACAGACAGGCGTATGACCCCGGATGAGATCGTTCTAGGCATACTCGTCCCACACTGCACCCATTGC\n",
      " is 0.2334\n",
      "----------------------------------------------------------------------------------------------------\n",
      "The mean-square distance (of nucleic acid proportions) between\n",
      " ACGATACACTGAATGACAGCAGTCACTGACAGTAGTACGAGTAGTAGCAGAGAGTAATAAAGAATTAATATATGACACTACGAAAAAAATGCATCG\n",
      " and\n",
      " TAAAGCTTTAGAAGATGTCGCACCCTGTGCTAAAGCTTCGGCTGCCAGTTCAAGTACTAGATGAAACCTGATTATAAGCCACGCACTAACGGATCA\n",
      " is 0.1559\n",
      "----------------------------------------------------------------------------------------------------\n",
      "The minimum distance was found for the sequence number 3\n"
     ]
    }
   ],
   "source": [
    "least = 99\n",
    "least_idx = 0\n",
    "for i in range(3):\n",
    "    s = DiscreteDistribution({'A':0.25,'T':0.25,'G':0.25,'C':0.25})\n",
    "    s.fit(dna_seq[i])\n",
    "    sample_params = np.array(list(s.parameters[0].values()))\n",
    "    distance = np.sqrt(np.sum((dna_params-sample_params)**2))\n",
    "    if distance < least:\n",
    "        least = distance\n",
    "        least_idx = i\n",
    "    print(f\"The mean-square distance (of nucleic acid proportions) between\\n {dna_data}\\n and\\n {dna_seq[i]}\\n is {round(distance,4)}\")\n",
    "    print(\"-\"*100)\n",
    "    \n",
    "print(f\"The minimum distance was found for the sequence number {least_idx+1}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## Gaussian Mixture Models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "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 = numpy.concatenate([numpy.random.normal((8, 2), 1, size=(200, 2)),\n",
    "                       numpy.random.normal((2, 1), 1, size=(150, 2)),\n",
    "                       numpy.random.normal((4, 6), 1, size=(100, 2))])\n",
    "\n",
    "plt.scatter(X[:,0], X[:,1], color='blue',alpha=0.7,edgecolor='k')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model directly from the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "gmm = GeneralMixtureModel.from_samples(MultivariateGaussianDistribution, 3, X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[8.162352837131197, 1.8863014822295276]\n",
      "[4.0166748117763404, 6.101161649975762]\n",
      "[2.088473252570433, 1.0100230642239891]\n"
     ]
    }
   ],
   "source": [
    "for d in gmm.distributions:\n",
    "    print(d.parameters[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Probability densities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1008x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = numpy.arange(-1, 10.1, .1)\n",
    "y = numpy.arange(-1, 10.1, .1)\n",
    "\n",
    "xx, yy = numpy.meshgrid(x, y)\n",
    "x_ = numpy.array(list(zip(xx.flatten(), yy.flatten())))\n",
    "\n",
    "p1 = MultivariateGaussianDistribution.from_samples(X).probability(x_).reshape(len(x), len(y))\n",
    "p2 = gmm.probability(x_).reshape(len(x), len(y))\n",
    "\n",
    "\n",
    "plt.figure(figsize=(14, 6))\n",
    "plt.subplot(121)\n",
    "plt.contourf(xx, yy, p1, cmap='plasma', alpha=0.8)\n",
    "plt.scatter(X[:,0], X[:,1],color='blue',alpha=0.7,edgecolor='k')\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.contourf(xx, yy, p2, cmap='plasma', alpha=0.8)\n",
    "plt.scatter(X[:,0], X[:,1],color='blue',alpha=0.7,edgecolor='k')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Markov chain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "transition_table = [['Rainy', 'Sunny', 0.10],\n",
    "                                ['Rainy', 'Cloudy', 0.70],\n",
    "                                ['Rainy', 'Rainy', 0.20],\n",
    "                                ['Sunny', 'Sunny', 0.40],\n",
    "                                ['Sunny', 'Cloudy', 0.40],\n",
    "                                ['Sunny', 'Rainy', 0.20],\n",
    "                                ['Cloudy', 'Cloudy', 0.40],\n",
    "                                ['Cloudy', 'Rainy', 0.30],\n",
    "                                ['Cloudy', 'Sunny', 0.20]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "d1 = DiscreteDistribution({'Rainy': 0.20, 'Sunny': 0.50, 'Cloudy': 0.30})\n",
    "d2 = ConditionalProbabilityTable(transition_table, [d1])\n",
    "\n",
    "mc = MarkovChain([d1,d2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "from tabulate import tabulate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "t=tabulate(transition_table)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------  ------  ---\n",
      "Rainy   Sunny   0.1\n",
      "Rainy   Cloudy  0.7\n",
      "Rainy   Rainy   0.2\n",
      "Sunny   Sunny   0.4\n",
      "Sunny   Cloudy  0.4\n",
      "Sunny   Rainy   0.2\n",
      "Cloudy  Cloudy  0.4\n",
      "Cloudy  Rainy   0.3\n",
      "Cloudy  Sunny   0.2\n",
      "------  ------  ---\n"
     ]
    }
   ],
   "source": [
    "print(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.7646205525906047"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mc.log_probability(['Cloudy','Rainy','Cloudy'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-7.824046010856291"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mc.log_probability(['Rainy','Sunny','Rainy','Sunny'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rainy\tSunny\t0.10000000000000002\n",
      "Rainy\tCloudy\t0.7\n",
      "Rainy\tRainy\t0.2\n",
      "Sunny\tSunny\t0.4\n",
      "Sunny\tCloudy\t0.4\n",
      "Sunny\tRainy\t0.2\n",
      "Cloudy\tCloudy\t0.4\n",
      "Cloudy\tRainy\t0.3\n",
      "Cloudy\tSunny\t0.2\n"
     ]
    }
   ],
   "source": [
    "print(mc.distributions[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gen_days(length=100):\n",
    "    from random import choices\n",
    "    seq = '-'.join(choices(['Sunny','Rainy','Cloudy'],k=length))\n",
    "    return seq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rainy-Sunny-Rainy-Sunny-Rainy-Sunny-Rainy-Rainy-Sunny-Sunny-Sunny-Rainy-Sunny-Cloudy\n"
     ]
    }
   ],
   "source": [
    "mc_data = []\n",
    "for _ in range(1):\n",
    "    a = gen_days(14)\n",
    "    print(a)\n",
    "    b = a.split('-')\n",
    "    mc_data.append(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "mc.fit(mc_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rainy\tSunny\t0.8333333333333334\n",
      "Rainy\tCloudy\t0.0\n",
      "Rainy\tRainy\t0.16666666666666669\n",
      "Sunny\tSunny\t0.2857142857142857\n",
      "Sunny\tCloudy\t0.14285714285714285\n",
      "Sunny\tRainy\t0.5714285714285714\n",
      "Cloudy\tCloudy\t0.3333333333333333\n",
      "Cloudy\tRainy\t0.3333333333333333\n",
      "Cloudy\tSunny\t0.3333333333333333\n"
     ]
    }
   ],
   "source": [
    "print(mc.distributions[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "mc_data = []\n",
    "for _ in range(1):\n",
    "    a = gen_days(3650)\n",
    "    b = a.split('-')\n",
    "    mc_data.append(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rainy\tSunny\t0.3196457326892109\n",
      "Rainy\tCloudy\t0.3260869565217391\n",
      "Rainy\tRainy\t0.3542673107890499\n",
      "Sunny\tSunny\t0.33075601374570446\n",
      "Sunny\tCloudy\t0.3393470790378007\n",
      "Sunny\tRainy\t0.32989690721649484\n",
      "Cloudy\tCloudy\t0.3563958165728078\n",
      "Cloudy\tRainy\t0.336283185840708\n",
      "Cloudy\tSunny\t0.3073209975864843\n"
     ]
    }
   ],
   "source": [
    "mc.fit(mc_data)\n",
    "print(mc.distributions[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hidden Markov Model (HMM)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "d1 = DiscreteDistribution({'Harry': 0.25, 'Ron': 0.25, \n",
    "                           'Hagrid': 0.25, 'Dumbledore': 0.25})\n",
    "d2 = DiscreteDistribution({'Harry': 0.4, 'Ron': 0.10, \n",
    "                           'Hagrid': 0.1, 'Dumbledore': 0.4})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "s1 = State(d1, name='uniform')\n",
    "s2 = State(d2, name='Harry-Dumbledore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "hmm = HiddenMarkovModel()\n",
    "hmm.add_states(s1, s2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "hmm.add_transition(hmm.start, s1, 0.5)\n",
    "hmm.add_transition(hmm.start, s2, 0.5)\n",
    "hmm.add_transition(s1, s1, 0.9)\n",
    "hmm.add_transition(s1, s2, 0.1)\n",
    "hmm.add_transition(s2, s1, 0.1)\n",
    "hmm.add_transition(s2, s2, 0.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "hmm.bake()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "seq = 'Harry-Hagrid-Ron-Hagrid-Ron-Harry-\\\n",
    "Dumbledore-Harry-Dumbledore-Ron-\\\n",
    "Harry-Dumbledore-Hagrid-Dumbledore-Harry-\\\n",
    "Ron-Hagrid-Hagrid-Harry-\\\n",
    "Dumbledore-Hagrid-Harry-Dumbledore-Harry-\\\n",
    "Dumbledore-Ron-Dumbledore-Hagrid'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "seq = list(seq.split('-'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "hmm_predictions = hmm.predict(seq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1]\n"
     ]
    }
   ],
   "source": [
    "print(hmm_predictions)"
   ]
  }
 ],
 "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": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}