Use k-order Markov chains for infer models of data using CMPy

README.md

A example of using k-order Markov chain topologies for inference with CMPy.

Infer_Markov_Chain_Ex.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function, division\n",
    "\n",
    "# imports\n",
    "import cmpy\n",
    "import cmpy.inference.bayesianem as bayesem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Markov Chains in CMPy\n",
    "\n",
    "Markov chains are available as candidate topologies that can be passed to the general epsilon machine inference machinery. An example follows of iterating over all k=0,1 and 2 binary Markov Chains -- this just show the potential topologies that can be fitted to data.  However, in the real inference application the topology (order k) as well as the transition probabilities are all inferred from data passed to the code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# generate an example set of binary Markov chains\n",
    "binary_mcs_ex = []\n",
    "\n",
    "# args below:\n",
    "# 2 -- is the alphabet size\n",
    "# [0,1,2] -- are the orders k of the Markov Chain\n",
    "for mc in bayesem.MarkovChainGenerator(2, [0,1,2]):\n",
    "    # save to list for drawing below\n",
    "    binary_mcs_ex.append(mc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Couldn't import dot_parser, loading of dot files will not be possible.\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAO0AAABTCAYAAABzjYCKAAAABmJLR0QA/wD/AP+gvaeTAAAWX0lE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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# k=0\n",
    "binary_mcs_ex[0].draw(show='ipynb')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKYAAADbCAYAAADnNOpoAAAABmJLR0QA/wD/AP+gvaeTAAAgAElE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\nrkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# k=1\n",
    "binary_mcs_ex[1].draw(show='ipynb')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAc8AAAHrCAYAAACpRRYLAAAABmJLR0QA/wD/AP+gvaeTAAAgAElE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\nKlCSIzIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# k=2\n",
    "binary_mcs_ex[2].draw(show='ipynb')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Infer Markov chain data\n",
    "\n",
    "I'll start by inferring a Markov chain toplogy and parameters using the Markov chain generator shown above.  First, let's define the data-generator and generate some data. Notice that I've use some non-trivial probabilities to make it clear that actual inference is going on..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKYAAADbCAYAAADnNOpoAAAABmJLR0QA/wD/AP+gvaeTAAAgAElE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\nxTIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "target_str = (\"0 0 0 0.1;\"\n",
    "              \"0 1 1 0.9;\"\n",
    "              \"1 0 0 0.25;\"\n",
    "              \"1 1 1 0.75;\")\n",
    "target_mc = cmpy.machines.from_string(target_str)\n",
    "target_mc.draw(show='ipynb')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First ten symbols:  ['1', '1', '1', '1', '1', '1', '1', '1', '1', '0']\n"
     ]
    }
   ],
   "source": [
    "# generate data\n",
    "data = target_mc.symbols(1e4)\n",
    "print(\"First ten symbols: \", data[:10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "*Infer Machine Topology (InferEM)\n",
      " * Model Prior- beta: 0.00000\n",
      " * Inferring all machines...\n",
      "  ** 5 machines considered, 5 possible\n",
      " * Calculating log evidence for all machines...\n",
      " * Calculating model probabilities for all machines... \n",
      "\n"
     ]
    }
   ],
   "source": [
    "# candidate models: binary MCs with order k=0-4\n",
    "candidate_mcs = bayesem.MarkovChainGenerator(2, [n for n in range(5)])\n",
    "\n",
    "# instantiate the posterior\n",
    "mc_posterior = bayesem.ModelComparisonEM(candidate_mcs, data, verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Markov Chain: Order 0, 2 Symbols --- prob: 4.13973523243e-51\n",
      "Markov Chain: Order 1, 2 Symbols --- prob: 0.997217704061\n",
      "Markov Chain: Order 2, 2 Symbols --- prob: 0.00278217485659\n",
      "Markov Chain: Order 3, 2 Symbols --- prob: 1.21082275468e-07\n",
      "Markov Chain: Order 4, 2 Symbols --- prob: 2.96676162946e-14\n"
     ]
    }
   ],
   "source": [
    "# this should give Order 1 the highest probability\n",
    "posterior_probs = mc_posterior.model_probabilities()\n",
    "for mc in sorted(posterior_probs.keys()):\n",
    "    print(\"{} --- prob: {}\".format(mc, posterior_probs[mc]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epsilon Machine Inference\n",
      "* Machine: Markov Chain: Order 1, 2 Symbols\n",
      "* POSTERIOR -- data available\n",
      "\n",
      "** EVIDENCE TERMS\n",
      "*** logP(D|M): -5.186592e+03\n",
      "**** logP(D|0, M): -5.186506e+03 \n",
      "**** logP(D|1, M): -5.186685e+03 \n",
      "\n",
      "** PROBABILITY OF START STATES\n",
      "**** P(0|D, M): 5.445021e-01 \n",
      "**** P(1|D, M): 4.554979e-01 \n",
      "\n",
      "Dirichlet Distribution:\n",
      "**Possible start nodes: ['1', '0']\n",
      "**Data available -- posterior\n",
      " ** log P(D | s_i,0=1 , M_i) = -5.1866848448e+03\n",
      " ** log P(D | s_i,0=0 , M_i) = -5.1865063641e+03\n",
      "\n",
      "NODES\n",
      "*startNode 0\n",
      "0-sum a:    2  sum n: 2224\n",
      "1-sum a:    2  sum n: 7776\n",
      "*startNode 1\n",
      "0-sum a:    2  sum n: 2223\n",
      "1-sum a:    2  sum n: 7777\n",
      "\n",
      "EDGES\n",
      "*startNode 0\n",
      "('0', '0')-a:    1 n:  242 Exp[p(0|0)]:0.109164\n",
      "('0', '1')-a:    1 n: 1982 Exp[p(1|0)]:0.890836\n",
      "('1', '0')-a:    1 n: 1981 Exp[p(0|1)]:0.254821\n",
      "('1', '1')-a:    1 n: 5795 Exp[p(1|1)]:0.745179\n",
      "*startNode 1\n",
      "('0', '0')-a:    1 n:  242 Exp[p(0|0)]:0.109213\n",
      "('0', '1')-a:    1 n: 1981 Exp[p(1|0)]:0.890787\n",
      "('1', '0')-a:    1 n: 1981 Exp[p(0|1)]:0.254789\n",
      "('1', '1')-a:    1 n: 5796 Exp[p(1|1)]:0.745211\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# let's see what the model parameters look like\n",
    "# get the -list- of most probable models (there can be more than one...)\n",
    "# - in this case- there should be one Markov chain with all start states possible\n",
    "map_list = mc_posterior.get_MAP_InferEM()\n",
    "for pr, inferem in map_list:\n",
    "    # print the inference information\n",
    "    print(inferem.summary_string())\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['1', '0']\n"
     ]
    }
   ],
   "source": [
    "# get a dictionary of the best topology  & start-state combos\n",
    "pr, map_inferem = map_list[0]\n",
    "map_machines = map_inferem.get_PM_machines()\n",
    "map_machine_names = map_machines.keys()\n",
    "print(map_machine_names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "name-- Posterior Mean (PM) Machine, Start Node: 1, Top: Markov Chain: Order 1, 2 Symbols\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKYAAADbCAYAAADnNOpoAAAABmJLR0QA/wD/AP+gvaeTAAAgAElE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\nLYKC4t/8P9ZNlYKyRM/5AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# map machine 1\n",
    "mc1 = map_machine_names[0]\n",
    "print(\"name-- {}\".format(map_machines[mc1]))\n",
    "map_machines[mc1].draw(show='ipynb')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "name-- Posterior Mean (PM) Machine, Start Node: 0, Top: Markov Chain: Order 1, 2 Symbols\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKYAAADbCAYAAADnNOpoAAAABmJLR0QA/wD/AP+gvaeTAAAgAElE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\nLYKC4t/8P9ZNlYKyRM/5AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# map machine 2\n",
    "mc2 = map_machine_names[1]\n",
    "print(\"name-- {}\".format(map_machines[mc2]))\n",
    "map_machines[mc2].draw(show='ipynb')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SNS example\n",
    "\n",
    "Because Markov chains are full support, they can accept data from any source and find the best (Markov chain) model given the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKYAAADbCAYAAADnNOpoAAAABmJLR0QA/wD/AP+gvaeTAAAgAElE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\nGAO/aFqEHj1/5f8B7O40ahpd5LgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sns = cmpy.machines.SNS()\n",
    "sns.draw(show='ipynb')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First ten symbols:  ['1', '0', '1', '1', '1', '1', '0', '1', '1', '0']\n"
     ]
    }
   ],
   "source": [
    "# generate sns data\n",
    "sns_data = sns.symbols(1e4)\n",
    "print(\"First ten symbols: \", sns_data[:10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "*Infer Machine Topology (InferEM)\n",
      " * Model Prior- beta: 0.00000\n",
      " * Inferring all machines...\n",
      "  ** 5 machines considered, 5 possible\n",
      " * Calculating log evidence for all machines...\n",
      " * Calculating model probabilities for all machines... \n",
      "\n"
     ]
    }
   ],
   "source": [
    "# candidate models: binary MCs with order k=0-4\n",
    "# CAREFUL -- there are 2**k states for a k-order Markov chain\n",
    "#         -- keep maiximum k smallish\n",
    "sns_candidate_mcs = bayesem.MarkovChainGenerator(2, [n for n in range(5)])\n",
    "\n",
    "# instantiate the posterior\n",
    "sns_posterior = bayesem.ModelComparisonEM(sns_candidate_mcs, sns_data, verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Markov Chain: Order 0, 2 Symbols --- prob: 0.0\n",
      "Markov Chain: Order 1, 2 Symbols --- prob: 5.84734217258e-23\n",
      "Markov Chain: Order 2, 2 Symbols --- prob: 0.290075057027\n",
      "Markov Chain: Order 3, 2 Symbols --- prob: 0.709901112869\n",
      "Markov Chain: Order 4, 2 Symbols --- prob: 2.3830104195e-05\n"
     ]
    }
   ],
   "source": [
    "# this will give probs that depend on the amont of data used\n",
    "# and the orders of Markov chains used\n",
    "sns_posterior_probs = sns_posterior.model_probabilities()\n",
    "for mc in sorted(sns_posterior_probs.keys()):\n",
    "    print(\"{} --- prob: {}\".format(mc, sns_posterior_probs[mc]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epsilon Machine Inference\n",
      "* Machine: Markov Chain: Order 3, 2 Symbols\n",
      "* POSTERIOR -- data available\n",
      "\n",
      "** EVIDENCE TERMS\n",
      "*** logP(D|M): -4.727375e+03\n",
      "**** logP(D|000, M): -4.727330e+03 \n",
      "**** logP(D|001, M): -4.727752e+03 \n",
      "**** logP(D|010, M): -4.727332e+03 \n",
      "**** logP(D|011, M): -4.727278e+03 \n",
      "**** logP(D|100, M): -4.727330e+03 \n",
      "**** logP(D|101, M): -4.727346e+03 \n",
      "**** logP(D|110, M): -4.727331e+03 \n",
      "**** logP(D|111, M): -4.727378e+03 \n",
      "\n",
      "** PROBABILITY OF START STATES\n",
      "**** P(000|D, M): 1.308302e-01 \n",
      "**** P(001|D, M): 8.581106e-02 \n",
      "**** P(010|D, M): 1.305668e-01 \n",
      "**** P(011|D, M): 1.377937e-01 \n",
      "**** P(100|D, M): 1.308302e-01 \n",
      "**** P(101|D, M): 1.287339e-01 \n",
      "**** P(110|D, M): 1.307070e-01 \n",
      "**** P(111|D, M): 1.247269e-01 \n",
      "\n",
      "Dirichlet Distribution:\n",
      "**Possible start nodes: ['010', '011', '001', '000', '111', '110', '100', '101']\n",
      "**Data available -- posterior\n",
      " ** log P(D | s_i,0=010 , M_i) = -4.7273317807e+03\n",
      " ** log P(D | s_i,0=011 , M_i) = -4.7272779080e+03\n",
      " ** log P(D | s_i,0=001 , M_i) = -4.7277515180e+03\n",
      " ** log P(D | s_i,0=000 , M_i) = -4.7273297653e+03\n",
      " ** log P(D | s_i,0=111 , M_i) = -4.7273775391e+03\n",
      " ** log P(D | s_i,0=110 , M_i) = -4.7273307075e+03\n",
      " ** log P(D | s_i,0=100 , M_i) = -4.7273297653e+03\n",
      " ** log P(D | s_i,0=101 , M_i) = -4.7273459183e+03\n",
      "\n",
      "NODES\n",
      "*startNode 000\n",
      "000-sum a:    2  sum n:    1\n",
      "001-sum a:    2  sum n:    1\n",
      "010-sum a:    2  sum n:  619\n",
      "011-sum a:    2  sum n: 1857\n",
      "100-sum a:    2  sum n: None\n",
      "101-sum a:    2  sum n: 2475\n",
      "110-sum a:    2  sum n: 1856\n",
      "111-sum a:    2  sum n: 3191\n",
      "*startNode 001\n",
      "000-sum a:    2  sum n: None\n",
      "001-sum a:    2  sum n:    1\n",
      "010-sum a:    2  sum n:  618\n",
      "011-sum a:    2  sum n: 1858\n",
      "100-sum a:    2  sum n: None\n",
      "101-sum a:    2  sum n: 2475\n",
      "110-sum a:    2  sum n: 1857\n",
      "111-sum a:    2  sum n: 3191\n",
      "*startNode 010\n",
      "000-sum a:    2  sum n: None\n",
      "001-sum a:    2  sum n: None\n",
      "010-sum a:    2  sum n:  620\n",
      "011-sum a:    2  sum n: 1857\n",
      "100-sum a:    2  sum n: None\n",
      "101-sum a:    2  sum n: 2476\n",
      "110-sum a:    2  sum n: 1856\n",
      "111-sum a:    2  sum n: 3191\n",
      "*startNode 011\n",
      "000-sum a:    2  sum n: None\n",
      "001-sum a:    2  sum n: None\n",
      "010-sum a:    2  sum n:  618\n",
      "011-sum a:    2  sum n: 1858\n",
      "100-sum a:    2  sum n: None\n",
      "101-sum a:    2  sum n: 2475\n",
      "110-sum a:    2  sum n: 1857\n",
      "111-sum a:    2  sum n: 3192\n",
      "*startNode 100\n",
      "000-sum a:    2  sum n: None\n",
      "001-sum a:    2  sum n:    1\n",
      "010-sum a:    2  sum n:  619\n",
      "011-sum a:    2  sum n: 1857\n",
      "100-sum a:    2  sum n:    1\n",
      "101-sum a:    2  sum n: 2475\n",
      "110-sum a:    2  sum n: 1856\n",
      "111-sum a:    2  sum n: 3191\n",
      "*startNode 101\n",
      "000-sum a:    2  sum n: None\n",
      "001-sum a:    2  sum n: None\n",
      "010-sum a:    2  sum n:  618\n",
      "011-sum a:    2  sum n: 1858\n",
      "100-sum a:    2  sum n: None\n",
      "101-sum a:    2  sum n: 2476\n",
      "110-sum a:    2  sum n: 1857\n",
      "111-sum a:    2  sum n: 3191\n",
      "*startNode 110\n",
      "000-sum a:    2  sum n: None\n",
      "001-sum a:    2  sum n: None\n",
      "010-sum a:    2  sum n:  619\n",
      "011-sum a:    2  sum n: 1857\n",
      "100-sum a:    2  sum n: None\n",
      "101-sum a:    2  sum n: 2476\n",
      "110-sum a:    2  sum n: 1857\n",
      "111-sum a:    2  sum n: 3191\n",
      "*startNode 111\n",
      "000-sum a:    2  sum n: None\n",
      "001-sum a:    2  sum n: None\n",
      "010-sum a:    2  sum n:  618\n",
      "011-sum a:    2  sum n: 1857\n",
      "100-sum a:    2  sum n: None\n",
      "101-sum a:    2  sum n: 2475\n",
      "110-sum a:    2  sum n: 1857\n",
      "111-sum a:    2  sum n: 3193\n",
      "\n",
      "EDGES\n",
      "*startNode 000\n",
      "('000', '0')-a:    1 n: None Exp[p(0|000)]:0.333333\n",
      "('000', '1')-a:    1 n:    1 Exp[p(1|000)]:0.666667\n",
      "('001', '0')-a:    1 n:    1 Exp[p(0|001)]:0.666667\n",
      "('001', '1')-a:    1 n: None Exp[p(1|001)]:0.333333\n",
      "('010', '0')-a:    1 n: None Exp[p(0|010)]:0.001610\n",
      "('010', '1')-a:    1 n:  619 Exp[p(1|010)]:0.998390\n",
      "('011', '0')-a:    1 n:  608 Exp[p(0|011)]:0.327595\n",
      "('011', '1')-a:    1 n: 1249 Exp[p(1|011)]:0.672405\n",
      "('100', '0')-a:    1 n: None Exp[p(0|100)]:0.500000\n",
      "('100', '1')-a:    1 n: None Exp[p(1|100)]:0.500000\n",
      "('101', '0')-a:    1 n:  618 Exp[p(0|101)]:0.249899\n",
      "('101', '1')-a:    1 n: 1857 Exp[p(1|101)]:0.750101\n",
      "('110', '0')-a:    1 n: None Exp[p(0|110)]:0.000538\n",
      "('110', '1')-a:    1 n: 1856 Exp[p(1|110)]:0.999462\n",
      "('111', '0')-a:    1 n: 1248 Exp[p(0|111)]:0.391168\n",
      "('111', '1')-a:    1 n: 1943 Exp[p(1|111)]:0.608832\n",
      "*startNode 001\n",
      "('000', '0')-a:    1 n: None Exp[p(0|000)]:0.500000\n",
      "('000', '1')-a:    1 n: None Exp[p(1|000)]:0.500000\n",
      "('001', '0')-a:    1 n: None Exp[p(0|001)]:0.333333\n",
      "('001', '1')-a:    1 n:    1 Exp[p(1|001)]:0.666667\n",
      "('010', '0')-a:    1 n: None Exp[p(0|010)]:0.001613\n",
      "('010', '1')-a:    1 n:  618 Exp[p(1|010)]:0.998387\n",
      "('011', '0')-a:    1 n:  609 Exp[p(0|011)]:0.327957\n",
      "('011', '1')-a:    1 n: 1249 Exp[p(1|011)]:0.672043\n",
      "('100', '0')-a:    1 n: None Exp[p(0|100)]:0.500000\n",
      "('100', '1')-a:    1 n: None Exp[p(1|100)]:0.500000\n",
      "('101', '0')-a:    1 n:  618 Exp[p(0|101)]:0.249899\n",
      "('101', '1')-a:    1 n: 1857 Exp[p(1|101)]:0.750101\n",
      "('110', '0')-a:    1 n: None Exp[p(0|110)]:0.000538\n",
      "('110', '1')-a:    1 n: 1857 Exp[p(1|110)]:0.999462\n",
      "('111', '0')-a:    1 n: 1248 Exp[p(0|111)]:0.391168\n",
      "('111', '1')-a:    1 n: 1943 Exp[p(1|111)]:0.608832\n",
      "*startNode 010\n",
      "('000', '0')-a:    1 n: None Exp[p(0|000)]:0.500000\n",
      "('000', '1')-a:    1 n: None Exp[p(1|000)]:0.500000\n",
      "('001', '0')-a:    1 n: None Exp[p(0|001)]:0.500000\n",
      "('001', '1')-a:    1 n: None Exp[p(1|001)]:0.500000\n",
      "('010', '0')-a:    1 n: None Exp[p(0|010)]:0.001608\n",
      "('010', '1')-a:    1 n:  620 Exp[p(1|010)]:0.998392\n",
      "('011', '0')-a:    1 n:  608 Exp[p(0|011)]:0.327595\n",
      "('011', '1')-a:    1 n: 1249 Exp[p(1|011)]:0.672405\n",
      "('100', '0')-a:    1 n: None Exp[p(0|100)]:0.500000\n",
      "('100', '1')-a:    1 n: None Exp[p(1|100)]:0.500000\n",
      "('101', '0')-a:    1 n:  619 Exp[p(0|101)]:0.250202\n",
      "('101', '1')-a:    1 n: 1857 Exp[p(1|101)]:0.749798\n",
      "('110', '0')-a:    1 n: None Exp[p(0|110)]:0.000538\n",
      "('110', '1')-a:    1 n: 1856 Exp[p(1|110)]:0.999462\n",
      "('111', '0')-a:    1 n: 1248 Exp[p(0|111)]:0.391168\n",
      "('111', '1')-a:    1 n: 1943 Exp[p(1|111)]:0.608832\n",
      "*startNode 011\n",
      "('000', '0')-a:    1 n: None Exp[p(0|000)]:0.500000\n",
      "('000', '1')-a:    1 n: None Exp[p(1|000)]:0.500000\n",
      "('001', '0')-a:    1 n: None Exp[p(0|001)]:0.500000\n",
      "('001', '1')-a:    1 n: None Exp[p(1|001)]:0.500000\n",
      "('010', '0')-a:    1 n: None Exp[p(0|010)]:0.001613\n",
      "('010', '1')-a:    1 n:  618 Exp[p(1|010)]:0.998387\n",
      "('011', '0')-a:    1 n:  608 Exp[p(0|011)]:0.327419\n",
      "('011', '1')-a:    1 n: 1250 Exp[p(1|011)]:0.672581\n",
      "('100', '0')-a:    1 n: None Exp[p(0|100)]:0.500000\n",
      "('100', '1')-a:    1 n: None Exp[p(1|100)]:0.500000\n",
      "('101', '0')-a:    1 n:  618 Exp[p(0|101)]:0.249899\n",
      "('101', '1')-a:    1 n: 1857 Exp[p(1|101)]:0.750101\n",
      "('110', '0')-a:    1 n: None Exp[p(0|110)]:0.000538\n",
      "('110', '1')-a:    1 n: 1857 Exp[p(1|110)]:0.999462\n",
      "('111', '0')-a:    1 n: 1249 Exp[p(0|111)]:0.391359\n",
      "('111', '1')-a:    1 n: 1943 Exp[p(1|111)]:0.608641\n",
      "*startNode 100\n",
      "('000', '0')-a:    1 n: None Exp[p(0|000)]:0.500000\n",
      "('000', '1')-a:    1 n: None Exp[p(1|000)]:0.500000\n",
      "('001', '0')-a:    1 n:    1 Exp[p(0|001)]:0.666667\n",
      "('001', '1')-a:    1 n: None Exp[p(1|001)]:0.333333\n",
      "('010', '0')-a:    1 n: None Exp[p(0|010)]:0.001610\n",
      "('010', '1')-a:    1 n:  619 Exp[p(1|010)]:0.998390\n",
      "('011', '0')-a:    1 n:  608 Exp[p(0|011)]:0.327595\n",
      "('011', '1')-a:    1 n: 1249 Exp[p(1|011)]:0.672405\n",
      "('100', '0')-a:    1 n: None Exp[p(0|100)]:0.333333\n",
      "('100', '1')-a:    1 n:    1 Exp[p(1|100)]:0.666667\n",
      "('101', '0')-a:    1 n:  618 Exp[p(0|101)]:0.249899\n",
      "('101', '1')-a:    1 n: 1857 Exp[p(1|101)]:0.750101\n",
      "('110', '0')-a:    1 n: None Exp[p(0|110)]:0.000538\n",
      "('110', '1')-a:    1 n: 1856 Exp[p(1|110)]:0.999462\n",
      "('111', '0')-a:    1 n: 1248 Exp[p(0|111)]:0.391168\n",
      "('111', '1')-a:    1 n: 1943 Exp[p(1|111)]:0.608832\n",
      "*startNode 101\n",
      "('000', '0')-a:    1 n: None Exp[p(0|000)]:0.500000\n",
      "('000', '1')-a:    1 n: None Exp[p(1|000)]:0.500000\n",
      "('001', '0')-a:    1 n: None Exp[p(0|001)]:0.500000\n",
      "('001', '1')-a:    1 n: None Exp[p(1|001)]:0.500000\n",
      "('010', '0')-a:    1 n: None Exp[p(0|010)]:0.001613\n",
      "('010', '1')-a:    1 n:  618 Exp[p(1|010)]:0.998387\n",
      "('011', '0')-a:    1 n:  609 Exp[p(0|011)]:0.327957\n",
      "('011', '1')-a:    1 n: 1249 Exp[p(1|011)]:0.672043\n",
      "('100', '0')-a:    1 n: None Exp[p(0|100)]:0.500000\n",
      "('100', '1')-a:    1 n: None Exp[p(1|100)]:0.500000\n",
      "('101', '0')-a:    1 n:  618 Exp[p(0|101)]:0.249798\n",
      "('101', '1')-a:    1 n: 1858 Exp[p(1|101)]:0.750202\n",
      "('110', '0')-a:    1 n: None Exp[p(0|110)]:0.000538\n",
      "('110', '1')-a:    1 n: 1857 Exp[p(1|110)]:0.999462\n",
      "('111', '0')-a:    1 n: 1248 Exp[p(0|111)]:0.391168\n",
      "('111', '1')-a:    1 n: 1943 Exp[p(1|111)]:0.608832\n",
      "*startNode 110\n",
      "('000', '0')-a:    1 n: None Exp[p(0|000)]:0.500000\n",
      "('000', '1')-a:    1 n: None Exp[p(1|000)]:0.500000\n",
      "('001', '0')-a:    1 n: None Exp[p(0|001)]:0.500000\n",
      "('001', '1')-a:    1 n: None Exp[p(1|001)]:0.500000\n",
      "('010', '0')-a:    1 n: None Exp[p(0|010)]:0.001610\n",
      "('010', '1')-a:    1 n:  619 Exp[p(1|010)]:0.998390\n",
      "('011', '0')-a:    1 n:  608 Exp[p(0|011)]:0.327595\n",
      "('011', '1')-a:    1 n: 1249 Exp[p(1|011)]:0.672405\n",
      "('100', '0')-a:    1 n: None Exp[p(0|100)]:0.500000\n",
      "('100', '1')-a:    1 n: None Exp[p(1|100)]:0.500000\n",
      "('101', '0')-a:    1 n:  619 Exp[p(0|101)]:0.250202\n",
      "('101', '1')-a:    1 n: 1857 Exp[p(1|101)]:0.749798\n",
      "('110', '0')-a:    1 n: None Exp[p(0|110)]:0.000538\n",
      "('110', '1')-a:    1 n: 1857 Exp[p(1|110)]:0.999462\n",
      "('111', '0')-a:    1 n: 1248 Exp[p(0|111)]:0.391168\n",
      "('111', '1')-a:    1 n: 1943 Exp[p(1|111)]:0.608832\n",
      "*startNode 111\n",
      "('000', '0')-a:    1 n: None Exp[p(0|000)]:0.500000\n",
      "('000', '1')-a:    1 n: None Exp[p(1|000)]:0.500000\n",
      "('001', '0')-a:    1 n: None Exp[p(0|001)]:0.500000\n",
      "('001', '1')-a:    1 n: None Exp[p(1|001)]:0.500000\n",
      "('010', '0')-a:    1 n: None Exp[p(0|010)]:0.001613\n",
      "('010', '1')-a:    1 n:  618 Exp[p(1|010)]:0.998387\n",
      "('011', '0')-a:    1 n:  608 Exp[p(0|011)]:0.327595\n",
      "('011', '1')-a:    1 n: 1249 Exp[p(1|011)]:0.672405\n",
      "('100', '0')-a:    1 n: None Exp[p(0|100)]:0.500000\n",
      "('100', '1')-a:    1 n: None Exp[p(1|100)]:0.500000\n",
      "('101', '0')-a:    1 n:  618 Exp[p(0|101)]:0.249899\n",
      "('101', '1')-a:    1 n: 1857 Exp[p(1|101)]:0.750101\n",
      "('110', '0')-a:    1 n: None Exp[p(0|110)]:0.000538\n",
      "('110', '1')-a:    1 n: 1857 Exp[p(1|110)]:0.999462\n",
      "('111', '0')-a:    1 n: 1249 Exp[p(0|111)]:0.391236\n",
      "('111', '1')-a:    1 n: 1944 Exp[p(1|111)]:0.608764\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# let's see what the model parameters look like\n",
    "# get the -list- of most probable models (there can be more than one...)\n",
    "sns_map_list = sns_posterior.get_MAP_InferEM()\n",
    "for pr, inferem in sns_map_list:\n",
    "    # print the inference information\n",
    "    print(inferem.summary_string())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['010', '011', '001', '000', '111', '110', '100', '101']\n"
     ]
    }
   ],
   "source": [
    "# get a dictionary of the best topology  & start-state combos\n",
    "pr, sns_map_inferem = sns_map_list[0]\n",
    "sns_map_machines = sns_map_inferem.get_PM_machines()\n",
    "sns_map_machine_names = sns_map_machines.keys()\n",
    "print(sns_map_machine_names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "name-- Posterior Mean (PM) Machine, Start Node: 011, Top: Markov Chain: Order 3, 2 Symbols\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAksAAAQLCAYAAACbNe1UAAAABmJLR0QA/wD/AP+gvaeTAAAgAElE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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# map machine 1\n",
    "# -- I'll just do this one, for start state 011\n",
    "# -- Obviously there are more, as seen above\n",
    "sns_mc1 = '011'\n",
    "print(\"name-- {}\".format(sns_map_machines[sns_mc1]))\n",
    "sns_map_machines[sns_mc1].draw(show='ipynb')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}