{ "metadata": { "name": "", "signature": "sha256:c9f5a9649c7242a9179da0d0d009c8ae64a5d5037b3b9a35c83413c8309613b6" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "#Determining the posterior probabilities using YAHMM\n", "\n", "*by [Tamas Nagy](http://www.tamasnagy.com)*\n", "\n", "
\n", "\n", "When working with Hidden Markov Models (HMMs), we are often interested in determining the \"optimal\" sequence of hidden states $Q = q_1q_2...q_N$ given a set of observations $O = O_1O_2...O_N$ and a model $\\lambda$. So how do we find the optimal sequence? Well, it depends on our definition of optimality. \n", "\n", "One option is to maximize the probability of entire state sequence $Q$ given $O$ and $\\lambda$. This is idea behind the Viterbi algorithm. However, we often find that the most probable path can be quite off for individual observations. \n", "\n", "An alternative is to defined optimality as maximizing the number of states $q_k$ that are individually most likely. Thus, our focus here is to be as correct as possible for each position separately, ignoring the rest of the sequence. However, this definintion also has a major drawback: the state sequence created in this manner may not even be a valid state sequence! \n", "\n", "For this reason it is often helpful to use both methods for interrogating the results of a model." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from yahmm import *\n", "import seaborn as sns, numpy as np\n", "from matplotlib.patches import Rectangle\n", "from __future__ import division, print_function\n", "\n", "# %install_ext https://raw.githubusercontent.com/rasbt/python_reference/master/ipython_magic/watermark.py\n", "%load_ext watermark\n", "%watermark -t -d -z -p yahmm,seaborn,numpy,matplotlib" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "20/07/2014 17:03:57 CEST\n", "\n", "yahmm 1.0.0\n", "seaborn 0.3.1\n", "numpy 1.8.1\n", "matplotlib 1.3.1\n" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this example, we will be reproducing Figure 2 from \"Hidden Markov Models for Prediction of Protein Features\" by Bystroff and Krogh. The model here is a simple two-state one for predicting transmembrane regions of proteins using the amino acid bias present in these regions. Transmembrane domains generally have a higher frequencies of hydrophobic residues (especially leucine and isoleucine) and lower frequencies of charged and polar residues. The model will have two states: one for transmembrane regions and one for other regions. The model will be initialized in the other state and will be infinite (i.e. no end state). \n", "\n", "Tables 1 and 2 provide the necessary emission and transition probabilities" ] }, { "cell_type": "code", "collapsed": false, "input": [ "aas = list('IFLVMWAYGCTSPHNQDEKR')\n", "tm_freq = np.array([1826,1370,2562,1751,616,414,1657,615,1243,\n", " 289,755,806,423,121,250,141,104,110,78,83])/15214\n", "other_freq = np.array([2187,1854,4156,2935,1201,819,3382,1616,\n", " 3352,960,2852,3410,2640,1085,2279,2054,\n", " 2551,2983,2651,2933]) / 47900\n", "\n", "# Add emission frequencies to states\n", "_m = State(DiscreteDistribution(dict(zip(aas, tm_freq))), name='M')\n", "_x = State(DiscreteDistribution(dict(zip(aas, other_freq))), name='X')\n", "\n", "model = Model('TransmembraneDomainPrediction', start=_x)\n", "\n", "# Transition frequencies from Table 2\n", "model.add_transition(_m, _x, 0.046)\n", "model.add_transition(_m, _m, 0.954)\n", "model.add_transition(_x, _x, 0.982)\n", "model.add_transition(_x, _m, 0.015)\n", "\n", "model.bake(verbose=True)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "TransmembraneDomainPrediction : X summed to 0.997, normalized to 1.0\n" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "For comparability, we will also use the sequence of a human Alpha-1D adrenergic receptor (Uniprot-Acc: [P25100](http://uniprot.org/uniprot/P25100)). Uniprot reports seven separate transmembrane regions for this proteins. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "ada1d_seq = list('MTFRDLLSVSFEGPRPDSSAGGSSAGGGGGSAGGAAPSEGPAVGGVPGGAGGGGGVVGAG\\\n", "SGEDNRSSAGEPGSAGAGGDVNGTAAVGGLVVSAQGVGVGVFLAAFILMAVAGNLLVILS\\\n", "VACNRHLQTVTNYFIVNLAVADLLLSATVLPFSATMEVLGFWAFGRAFCDVWAAVDVLCC\\\n", "TASILSLCTISVDRYVGVRHSLKYPAIMTERKAAAILALLWVVALVVSVGPLLGWKEPVP\\\n", "PDERFCGITEEAGYAVFSSVCSFYLPMAVIVVMYCRVYVVARSTTRSLEAGVKRERGKAS\\\n", "EVVLRIHCRGAATGADGAHGMRSAKGHTFRSSLSVRLLKFSREKKAAKTLAIVVGVFVLC\\\n", "WFPFFFVLPLGSLFPQLKPSEGVFKVIFWLGYFNSCVNPLIYPCSSREFKRAFLRLLRCQ\\\n", "CRRRRRRRPLWRVYGHHWRASTSGLRQDCAPSSGDAPPGAPLALTALPDPDPEPPGTPEM\\\n", "QAPVASRRKPPSAFREWRLLGPFRRPTTQLRAKVSSLSHKIRAGGAQRAEAACAQRSEVE\\\n", "AVSLGVPHEVAEGATCQAYELADYSNLRETDI')\n", "\n", "actual_transmems = [(96,121),(134,159),(170,192),(214,238),\n", " (252,275),(349,373),(381,405)]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's first get the most probable path using Viterbi and find the start and end states of the viterbi predicted regions" ] }, { "cell_type": "code", "collapsed": false, "input": [ "viterbi_path = model.viterbi(ada1d_seq)[1]\n", "\n", "viterbi_pred = np.array([state[1].name for state in viterbi_path[1:]])\n", "\n", "viterbi_pred_mem = viterbi_pred == 'M'\n", "starts = np.nonzero(viterbi_pred_mem & ~np.roll(viterbi_pred_mem, 1))[0]\n", "ends = np.nonzero(viterbi_pred_mem & ~np.roll(viterbi_pred_mem, -1))[0]\n", "transmems = zip(starts, ends)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's calculate the posterior probabilities $\\gamma_1\\gamma_2...\\gamma_k...\\gamma_N$ for being in state $S_i$ for each observation $k$. So for each position $k$, we'll calculate: \n", "\n", "$$ \\gamma_k(i) = \\frac{\\alpha_k(i)\\beta_k(i)}{\\sum_{i}^M \\alpha_k(i)\\beta_k(i)} $$\n", "\n", "where $M$ here is the number of states and the $\\alpha_k(i)\\beta_k(i)$ term are probabilities given by the forward-backward algorithm. In our simple example, $M=2$ for the two states (transmembrane and other), but this technique can be applied to more complex models as well. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "trans, ems = model.forward_backward(ada1d_seq)\n", "ems = np.exp(ems)\n", "probs = ems/np.sum(ems, axis=1)[:, np.newaxis]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let's plot everything. We'll need to plot the true transmembrane regions, the viterbi-predicted regions, and the posterior probabilities" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "colors = sns.color_palette('deep', n_colors=6, desat=0.5)\n", "sns.set_context(rc={\"figure.figsize\": (14, 6)})\n", "sns.plt.axhline(y=1.1, c=colors[0], alpha=0.7)\n", "sns.plt.axhline(y=0.5, c=colors[1], alpha=0.7)\n", "sns.plt.xlim([1, len(ada1d_seq)+1])\n", "sns.plt.ylim([0,1.2])\n", "sns.plt.ylabel(r'posterior probs, $\\gamma_k$')\n", "sns.plt.xlabel(r'$k$')\n", "axis = sns.plt.gca()\n", "\n", "# Plot viterbi predicted TMDs\n", "for start, end in transmems:\n", " axis.add_patch(Rectangle((start+1, 1.075), end-start+1, 0.05, \n", " facecolor=colors[0], alpha=0.7))\n", " axis.text(480,1.13, 'viterbi')\n", "\n", "# Plot actual TMDs\n", "for start, end in actual_transmems:\n", " axis.add_patch(Rectangle((start+1, .475), end-start+1, 0.05, \n", " facecolor=colors[1], alpha=0.7))\n", " axis.text(480, .53, 'actual')\n", "\n", "# Get indices of states\n", "indices = { state.name: i for i, state in enumerate( model.states ) }\n", "\n", "sns.plt.plot(range(1, len(ada1d_seq)+1), probs[:, indices['M']], \n", " c=colors[2], alpha=0.7)\n", "sns.plt.gcf().savefig('posteriors.png')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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4XXFsHMO2qbb2PZILxX3l3M7n8TOfIVonPzzc9Xo/K5dTyVyf8GNsHnI5+eFm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"text": [ "" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, the posterior probabilities are much better at recapitulating the transmembrane regions from the sequence than the viterbi output. Both techniques are useful in helping us understand and analyze our data, but they answer different questions. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
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\n", "\n", "Found an error? Found five? Was something not clear? Let us know at https://github.com/jmschrei/yahmm/issues. Even better? Submit a pull request! \n", "\n", "
\n", "\n", "(words of encouragement are welcome too!)" ] } ], "metadata": {} } ] }