{ "cells": [ { "cell_type": "markdown", "id": "f5efac92", "metadata": {}, "source": [ "# ShortestDistance and Forward-Backward" ] }, { "cell_type": "markdown", "id": "30301cdd", "metadata": {}, "source": [ "This worksheet shows how to use the `ShortestDistance` and `Reverse` operations, together\n", "with log weights, to obtain the equivalent of the forward-backward algorithm for Hidden Markov Models." ] }, { "cell_type": "code", "execution_count": 82, "id": "eb41e75b", "metadata": { "collapsed": false }, "outputs": [], "source": [ "from pylab import *\n", "import openfst\n", "from openfst import StdVectorFst as FST\n", "from openfst import LogVectorFst as LFST\n", "from fstutils import *\n", "figsize(12,4)" ] }, { "cell_type": "markdown", "id": "12ebe7ab", "metadata": {}, "source": [ "# Combining Weights" ] }, { "cell_type": "markdown", "id": "8edc67dc", "metadata": {}, "source": [ "Let's look at the effects of different weights in some simple example.\n", "\n", "Here, we consider an FST in which there are two identical paths with identical weights.\n", "How do they get combined, for example under minimization?" ] }, { "cell_type": "markdown", "id": "f2ae50d8", "metadata": {}, "source": [ "## Log Probabilities" ] }, { "cell_type": "code", "execution_count": 84, "id": "e581c663", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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K5bIEBASQnp7O2bNnef3114WkLVvf5/7+/vz7v/87Go2G3Nxcamtr0Wq1wtT0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\nIAgTjgiCBUEQBEEQhAnnfwHB3Hw7HgZQgQAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lf = LFST()\n", "lf.AddString(\"cat\",0.5,0.5)\n", "lf.AddString(\"cat\",1.0)\n", "show_fst(lf)" ] }, { "cell_type": "code", "execution_count": 85, "id": "caedd684", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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d3R1r1qzBzp07QUSYPn16h9kaRyCTyTB9+nQIBALw+Xwmyb3BYIDVasXVq1dx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\npVJh3rx5cHR0xL59+37xoH+gY4whOTkZBw8eRFB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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "dfst = LFST()\n", "openfst.Determinize(lf,dfst)\n", "openfst.Minimize(dfst)\n", "show_fst(dfst)" ] }, { "cell_type": "markdown", "id": "9b0a24c6", "metadata": {}, "source": [ "As we see here, the two paths get combined by probabilities. That is, each path\n", "can lead to the goal, and the total probability of reaching the goal is the\n", "sum of the probabilities for each path (in the log domain)." ] }, { "cell_type": "code", "execution_count": 66, "id": "b553a78a", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "-0.30685281944005466" ] }, "execution_count": 66, "metadata": {}, "output_type": "execute_result" } ], "source": [ "log(exp(-1.0)+exp(-1.0))" ] }, { "cell_type": "markdown", "id": "833baab4", "metadata": {}, "source": [ "## Costs and Minimization" ] }, { "cell_type": "markdown", "id": "63b8dce3", "metadata": {}, "source": [ "With the regular (log,+) semiring, the costs for each path get added along the path, but the total cost is just the minimum cost of reaching the goal." ] }, { "cell_type": "code", "execution_count": 86, "id": "98085f1b", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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K5bIEBASQnp7O2bNnef3114WkLVvf5/7+/vz7v/87Go2G3Nxcamtr0Wq1wtT0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\nIAgTjgiCBUEQBEEQhAnnfwHB3Hw7HgZQgQAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fst = FST()\n", "fst.AddString(\"cat\",0.5,0.5)\n", "fst.AddString(\"cat\",1.0)\n", "show_fst(lf)" ] }, { "cell_type": "code", "execution_count": 87, "id": "6e03b09c", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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QSCQStFothYWFyGQynE4nZ86cYXBwUAi7q6+v5+DBg0RHR7N58+bbfi1R7Irc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\nItkVBEEQBEEQZiyR7AqCIAiCIAgz1v8BGWUY8UMYQYIAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dfst = FST()\n", "openfst.Determinize(fst,dfst)\n", "openfst.Minimize(dfst)\n", "show_fst(dfst)" ] }, { "cell_type": "markdown", "id": "b37d172e", "metadata": {}, "source": [ "## Different Weights" ] }, { "cell_type": "markdown", "id": "a581050e", "metadata": {}, "source": [ "Tropical Semiring:\n", "\n", "- $\\oplus$: associative, commutative, $\\bar{0}$ as identity\n", "- $\\otimes$: associative, $\\bar{1}$ as identity" ] }, { "cell_type": "code", "execution_count": 69, "id": "1e11bd1a", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "::Weight *' at 0x33dd150> >" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "openfst.Weight()" ] }, { "cell_type": "code", "execution_count": 70, "id": "6d3041c9", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "::Weight *' at 0x33dd420> >" ] }, "execution_count": 70, "metadata": {}, "output_type": "execute_result" } ], "source": [ "openfst.LogWeight()" ] }, { "cell_type": "code", "execution_count": 71, "id": "3c828472", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "inf" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" } ], "source": [ "openfst.LogWeight.Zero().Value()" ] }, { "cell_type": "code", "execution_count": 72, "id": "50d0f510", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.0" ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "openfst.LogWeight.One().Value()" ] }, { "cell_type": "markdown", "id": "e6964ca9", "metadata": {}, "source": [ "Built-In Weights\n", "\n", "- Boolean\n", "- Real (probabilities)\n", "- Log (log probabilities)\n", "- Tropical (min,+)\n", "\n", "Note that you can get n-best paths by defining a new weight class that...\n", "\n", "- acts like a `Log` or `Tropical` weight\n", "- also keeps the n-best paths internally on combination" ] }, { "cell_type": "markdown", "id": "cda89204", "metadata": {}, "source": [ "# Viterbi" ] }, { "cell_type": "markdown", "id": "f5a2d99e", "metadata": {}, "source": [ "For getting the equivalent of the Viterbi algorithm, that is the shortest path,\n", "we need to use the semiring (min,+)." ] }, { "cell_type": "code", "execution_count": 73, "id": "6b722f3b", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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eRWJiIq5du4bs7GyT/OByuRyvvPIKxowZA39//wbV3WhBsK+vL6RSKfh8PoRC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\nAAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fst = FST()\n", "fst.AddString(\"cat\",1.0)\n", "fst.AddString(\"cot\",1.9)\n", "fst.AddString(\"car\",1.7)\n", "fst.AddString(\"dat\",1.3)\n", "dfst = FST()\n", "openfst.Determinize(fst,dfst)\n", "openfst.Minimize(dfst)\n", "fst = dfst\n", "show_fst(fst)" ] }, { "cell_type": "code", "execution_count": 74, "id": "3f2aeb6d", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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cRdXSeS6QSCQYDAYKCgqQyWS4XC7Onj1LX1+fEHZ3+fJlDh48SFRUFJs3b77j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\npBkzZozpNQ4NDWXevHmsXLmSRYsWodPp7sgI323V7DY0NLB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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "out = FST()\n", "openfst.ShortestPath(fst,out,1)\n", "show_fst(out)" ] }, { "cell_type": "markdown", "id": "f03c9346", "metadata": {}, "source": [ "# Forward Backward" ] }, { "cell_type": "markdown", "id": "a6c86fd8", "metadata": {}, "source": [ "For getting the equivalent of the forward-backward algorithm, we need to use log probabilities\n", "as weights." ] }, { "cell_type": "code", "execution_count": 75, "id": "94e92265", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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kp6dDqVRCV1cXbm5u8PX1hbe3Nzp37gxnZ+cW801nPJ8X2Z3MCGYwGAzGPwKp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\nLIQQQggh2p3/A7oPp11rY5bxAAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fst = LFST()\n", "fst.AddString(\"cat\",1.0)\n", "fst.AddString(\"cot\",1.9)\n", "fst.AddString(\"car\",1.7)\n", "fst.AddString(\"dat\",1.3)\n", "dfst = LFST()\n", "openfst.Determinize(fst,dfst)\n", "openfst.Minimize(dfst)\n", "fst = dfst\n", "show_fst(fst)" ] }, { "cell_type": "code", "execution_count": 76, "id": "a1eeda52", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0. 0.35644531 1.29980469 0.59667969 0.86252433 0.02775925]\n" ] } ], "source": [ "forward = openfst.vector_logweight()\n", "openfst.ShortestDistance(fst,forward)\n", "forward = array([v.Value() for v in forward])\n", "print forward" ] }, { "cell_type": "code", "execution_count": 77, "id": "cf1f8890", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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C8qHTZEawk5MTYmNjVYYp586dCzMzM8ydOxerV69GWVkZ/ve//zXYGdYIfjck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\nAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rfst = LFST()\n", "openfst.Reverse(fst,rfst)\n", "show_fst(rfst)" ] }, { "cell_type": "code", "execution_count": 78, "id": "f62e9646", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0. 0.02775919 0.00017603 0. 0.00019905 0. 0. ]\n" ] } ], "source": [ "reverse = openfst.vector_logweight()\n", "openfst.ShortestDistance(rfst,reverse)\n", "reverse = array([v.Value() for v in reverse])\n", "print reverse" ] }, { "cell_type": "code", "execution_count": 79, "id": "9f522160", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1.0, 0.70016076046423459, 0.27253077452703905, 0.55063689076056477, 0.42202093463650986, 0.94599457146783861]\n" ] } ], "source": [ "total = forward+reverse[1:][::-1]\n", "print [exp(-c) for c in total]" ] }, { "cell_type": "code", "execution_count": 80, "id": "d67cacf0", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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kp6dDqVRCV1cXbm5u8PX1hbe3Nzp37gxnZ+cW801nPJ8X2Z3MCGYwGAzGPwKp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Vu3ApCZmXnXF3JZWRkBAQHNWh5AaWkpNpuNVatW4eHhoU1FURdHVldXc/XqVb799tt6iyXVDsP/\n2l0Kbge6Xl5eGI1GDAYDPj4+eHl5odPp8PLywsPDA4PBgKenp3YtoGWr8Pb2RqfTYTAY0Ov12vX3\nC/Aa0zlSF4Y2dG6z2YDb03ZcLhe1tbXaVrV2ux243ZFQp+Ko53Wn6ag/S31UD7XDpSgKBoMBX19f\nbd67yWSiW7du9O3bF5PJVG8Bqdop+SFm80hISGD37t2cO3eOI0eOsGnTJmw2GyaTiR49emgpHUND\nQ+nQoQMBAQEN3pVxOp2UlZVRWlpKYWEhOTk5WCwWsrKyqKiowGg0kpCQwEsvvUS/fv0kd7oQrei+\nc4KnT5/O/v37CQ4O5vz58wC89dZbfPDBB1rPe/ny5fz0pz8Fbm/t+Oc//xlPT0/WrVvH6NGj6xcm\nc4KFuMuOHTtwuVz8+Mc/Jigo6J5ZKm7evEl8fDzp6enNvnOUxWLBarU2+F6vXr1aZNT0xIkTrF27\nli1bttzzNnbdUcy6C6rqjmY2NLqpvlZbW0t1dTVlZWVYrVYqKyuxWq24XC6qq6txuVzU1NRoAaYa\neKrZRtRr6s5hrampue/fsZqamnvO776TTqfD19dX+/+umwlAPTcajXh6emIwGLTA3Wg0otPpMBqN\n2kilumOjusOjj4+PFtx7enpqQbynp6f2XH1fDdz1en2bSS3YkhRFobKykpKSEgoLCzl+/DiZmZlc\nuHCB4uJi9Hq9Nq3DZDLh4eGBy+WioqJC68TV1tbSsWNH4uLiiI+PZ8iQIYSFhWE2m/H395d/ZyHc\n4KG2TT527Bj+/v6kpqZqQfCSJUswmUy89tpr9a69ePEiU6ZM4euvvyY/P5+nnnqKrKysel+eEgQL\n8XBeffVVdDod7733XovNDXaXhQsX0r17d+bMmSMBgWgTXC4XZWVl5OfnU1hYqO1Op96dUUfM1aki\ngYGBP5hpN0K0RQ+1MG7YsGFkZ2ff9XpDP3Dv3r2kpKRgMBiIiooiJiaGkydP8qMf/ajxtRZCNOjV\nV18lNTWVixcv0rdv39auTpOdO3eOo0ePMn36dAmARZvh4eFBhw4d6NChA3369Gnt6gghHlKTJiO9\n//77bNu2jYSEBN59913MZjMFBQX1At6IiAjy8/Pv+uxbb72lnQ8fPpzhw4c3pQpCtEsxMTGMHj2a\n7du3s3LlyjY5ymSz2Xj99dcZPXo0vXr1au3qCCGE+IHIyMggIyPjga9vdBA8e/Zs3nzzTQAWL17M\nggUL2LJlS4PXNjTCUzcIFkI03rRp00hLS+Ozzz5j7NixbWoktba2lo0bN+J0OvnNb37TJoN4IYQQ\nj6Y7B1eXLFly3+sb/Q0UHBysrcyeMWMGJ0+eBCA8PJzc3Fztury8vAdOWi6EeHCRkZEsWLCAuXPn\n8sUXX7R2dRrlyy+/5ODBg6xatQpfX9/Wro4QQoh2rNFBcGFhoXb+ySefaPMSk5KS2LVrF3a7HYvF\nwuXLlxk8eHDz1VQIAdyel/izn/2M1atXM3/+fL755pvWrtIDOXnyJNOnT2f27NkMGDCgtasjhBCi\nnbvvdIiUlBSOHDnCrVu3iIyMZMmSJWRkZHDmzBl0Oh3du3dn8+bNAMTGxpKcnExsbCx6vZ4NGza0\nqdu0QrQlHh4eJCUlce3aNebNm8fSpUt54oknMBgMrV21uzidTtLT01m1ahXLli1jwoQJ8rdBCCFE\nq7tvirRmL0xSpAnRrGw2G/v27WPlypU8++yzzJ49G39//9aulqa8vJyVK1eSmZnJ/Pnz78odLoQQ\nQrSUh8oT7O7KCCGapqioiKeffhpfX18++ugjQkNDW7tKnD9/ntTUVDw8PNi3bx9hYWGtXSUhhBDt\niATBQrQTN2/eZOPGjRw8eJBRo0YxYcIEt2/LarPZOHPmDLt37+b06dNMnDiROXPmPJLTNIQQQvyw\nSRAsRDvicrm4cOEC6enpfPrpp8TExJCWlsaIESNadIc5q9XK4cOH2bFjBzdv3mTixImMHTuW6Ojo\nNr+znRBCiLZJgmAh2qmqqirWrVvHpk2bMJlMzJw5k0mTJtGxY0cMBgOenp5NWqCmKAq1tbU4HA5K\nSkrYvn07W7dupbKykkWLFpGWlobJZGqB30gIIYR4cI9cEPzll1/KLnGiWWRkZEhbegC3bt3iyJEj\nZGRkkJ2dja+vLyEhIURHRxMREUHnzp0JDAzE398fo9GIwWBAp9PhcrlwOBzYbDbKy8spLy/nxo0b\n5ObmcuXKFW7evInVaqVHjx6MHDmSESNG4Ofn19q/bpNIWxLNQdqRaC7SlprH/wqC3TdZ8P+R/1jR\nXKQtPZjOnTszadIkxo8fT1FREbdu3SIvL49z585x8OBB8vPzKSkpoaKiAg8PD22EWFEUnE4niqIQ\nEBBAYGAgXbt2pXfv3vz85z8nNDSUTp060blz5za/85u0JdEcpB2J5iJtyT3cHgQLIVqHXq8nJCSE\nkJAQ4uLiGDNmTL33nU4nFRUVVFZW4nK50Ov1+Pn54efn59bFdUIIIYQ7yDebEAIAT09PzGYzZrO5\ntasihBBCtDi3zwkWQgghhBDCHR6ZOcGSGUIIIYQQQjwK2vZqFiGEEEIIIZpAgmAhhBBCCNHuuDUI\n/sc//kGvXr14/PHHefvtt91ZtGhjcnNzGTFiBHFxcfTp04d169YBUFxczKhRo+jRowejR4+mtLRU\n+8yKFSt4/PHH6dWrF4cOHWqtqotHlNPpJD4+nnHjxgHSlkTTlJaWMnnyZHr37k1sbCwnTpyQtiSa\nZMWKFcTFxdG3b1+mTJlCTU2NtCV3U9yktrZWiY6OViwWi2K325X+/fsrFy9edFfxoo0pLCxUMjMz\nFUVRlIqKCqVHjx7KxYsXlddff115++23FUVRlJUrVyqLFi1SFEVRLly4oPTv31+x2+2KxWJRoqOj\nFafT2Wr1F4+ed999V5kyZYoybtw4RVEUaUuiSVJTU5UtW7YoiqIoDodDKS0tlbYkGs1isSjdu3dX\nbDaboiiKkpycrPzlL3+RtuRmbhsJPnnyJDExMURFRWEwGHj22WfZu3evu4oXbUxoaCgDBgwAwN/f\nn969e5Ofn096ejppaWkApKWlsWfPHgD27t1LSkoKBoOBqKgoYmJiOHnyZKvVXzxa8vLyOHDgADNm\nzNAW6EpbEo1VVlbGsWPHmD59OnA793ZgYKC0JdFoAQEBGAwGqqurqa2tpbq6mrCwMGlLbua2IDg/\nP5/IyEjteUREBPn5+e4qXrRh2dnZZGZmkpiYyPXr1wkJCQEgJCSE69evA1BQUEBERIT2GWlfoq75\n8+ezatWqejvbSVsSjWWxWAgKCmLatGkMHDiQl156iaqqKmlLotE6duzIggUL6Nq1K2FhYZjNZkaN\nGiVtyc3cFgRLjmDRFJWVlUyaNIm1a9diMpnqvafT6e7brqTNCYBPP/2U4OBg4uPj75mmUdqSeBC1\ntbWcPn2aOXPmcPr0afz8/Fi5cmW9a6QtiQdx5coV1qxZQ3Z2NgUFBVRWVrJjx45610hbanluC4LD\nw8PJzc3Vnufm5tbr1QhxJ4fDwaRJk3j++eeZMGECcLtnfO3aNQAKCwsJDg4G7m5feXl5hIeHu7/S\n4pFz/Phx0tPT6d69OykpKXzxxRc8//zz0pZEo0VERBAREcETTzwBwOTJkzl9+jShoaHSlkSjnDp1\niiFDhtCpUyf0ej3PPPMM//rXv6QtuZnbguCEhAQuX75MdnY2drudv/3tbyQlJbmreNHGKIrCiy++\nSGxsLPPmzdNeT0pKYuvWrQBs3bpVC46TkpLYtWsXdrsdi8XC5cuXGTx4cKvUXTxali9fTm5uLhaL\nhV27djFy5Ei2b98ubUk0WmhoKJGRkWRlZQHw+eefExcXx7hx46QtiUbp1asX//73v7FarSiKwuef\nf05sbKy0JTdz245xer2e9evXM2bMGJxOJy+++CK9e/d2V/GijfnnP//Jjh076NevH/Hx8cDt9DC/\n+tWvSE5OZsuWLURFRbF7924AYmNjSU5OJjY2Fr1ez4YNG+RWkWiQ2i6kLYmmeP/993nuueew2+1E\nR0fz4Ycf4nQ6pS2JRunfvz+pqakkJCTg4eHBwIEDmTlzJhUVFdKW3Ein3GuSnBBCCCGEED9QsmOc\nEEIIIYRodyQIFkIIIYQQ7Y4EwUIIIYQQot2RIFgIIYQQQrQ7EgQLIYQQQoh2R4JgIYQQQgjR7kgQ\nLIQQQggh2p3/A7oPp11rY5bxAAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show_fst(fst)" ] }, { "cell_type": "markdown", "id": "174f4d74", "metadata": {}, "source": [ "# Baum Welch Training" ] }, { "cell_type": "markdown", "id": "f954ee5e", "metadata": {}, "source": [ "Given these algorithms, what would Baum Welch look like?" ] } ], "metadata": {}, "nbformat": 4, "nbformat_minor": 5 }