{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# ECE 417 Lecture 13: Baum-Welch/Expectation-Maximization for Training HMMs\n", "## Mark Hasegawa-Johnson, October 9, 2018\n", "This file is distributed under a CC-BY license. You may freely re-use or re-distribute the whole or any part. If you re-distribute a non-trivial portion of it, give me credit." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Outline of Today's lecture\n", "* Defining an HMM\n", "* Generating data from an HMM\n", "* Initializing the parameters\n", "* Re-estimating parameters: The forward-backward algorithm\n", "* The scaled forward-backward algorithm\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Preliminaries\n", "First let's load some libraries, and some data." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import scipy.stats as stats\n", "import requests\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Defining an HMM\n", "A diagonal covariance Gaussian Hidden Markov model (an HMM with diagonal covariance Gaussian observation probabilities) is defined by four sets of parameters:\n", "$$\\pi_i=\\Pr\\left\\{q_1=i\\right\\}$$\n", "$$a_{ij}=\\Pr\\left\\{q_{t+1}=j|q_t=i\\right\\}$$\n", "$$\\mu_{di}=E\\left[x_{dt}|q_t=i\\right]$$\n", "$$\\Sigma_{i}=E\\left[(\\vec{x}_{t}-\\vec\\mu_{i})(\\vec{x}_{t}-\\vec\\mu_{i})^T|q_t=i\\right]$$\n", "In this lecture I will generate data using the true values of each parameter, and then try to recognize data using estimated values of each parameter. Let's assume a three-state HMM.\n", "* For simplicity, let's set $\\pi_i=\\delta[i-1]$, so the HMM always starts in state 1.\n", "* Let's use a left-to-right HMM: $a_{ij}=0$ unless $j\\in\\left\\{i,i+1\\right\\}$. In particular, let's use $a_{ii}=0.8$, so that the HMM is expected to stay in each state for five frames.\n", "* Let's use a 12-dimensional observation vector. Its mean vector will be different in each state.\n", "* Let's use a variance vector which has the same variance in every dimension, but with higher variance in the middle state." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "states = [0,1,2,3]\n", "N = len(states)-1 # Define N as the number of emitting states\n", "pi_true = [1,0,0,0]\n", "A_true = [[0.8,0.2,0,0],[0,0.8,0.2,0],[0,0,0.8,0.2]]\n", "mu_true = [[2,2,2,2,0,0,0,0,0,0,0,0],[0,0,0,0,2,2,2,2,0,0,0,0],[0,0,0,0,0,0,0,0,2,2,2,2]]\n", "sigsq_true = [[1,1,1,1,1,1,1,1,1,1,1,1],[2,2,2,2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1,1,1,1,1]]\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "# Generating data from an HMM\n", "Now let's run the HMM. We'll generate a state $q$, then generate a vector $\\vec{x}$ from it. Then repeat this process until $q=3$, at which point we stop." ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5,1,'True State Sequence')" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Q = list(np.random.choice(states,1,p=pi_true))\n", "q = Q[-1]\n", "X = []\n", "while q < 3:\n", " xt = stats.multivariate_normal.rvs(mean=mu_true[q],cov=np.diag(sigsq_true[q]))\n", " X.append(xt)\n", " Q.extend(np.random.choice(states,1,p=A_true[q]))\n", " q = Q[-1]\n", "\n", "plt.figure(figsize=(15,5))\n", "plt.subplot(211)\n", "plt.imshow(np.transpose(X))\n", "plt.title('Generated feature vectors')\n", "plt.subplot(212)\n", "plt.plot(Q)\n", "plt.xlabel('Frames')\n", "plt.title('True State Sequence')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Estimating the parameters of an HMM\n", "Now let's create estimated parameters. In order to create the initial estimate,\n", "we'll just divide the training example into thirds. \n", "* pi: We'll assume we know this\n", "* A: We'll estimate this by estimating the duration of each state to be $d=T/3$, and then choosing the transition probability $a_{i,i+1}=1/d$. That's the transition probability such that the expected duration of the state is $d$.\n", "* $\\mu$, $\\sigma^2$: We'll estimate these parameters as the mean and the variance, respectively, of each one-third of the given training example.\n" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5,0,'Feature dimension')" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pi=[1,0,0,0]\n", "T=len(X)\n", "d=int(T/3)\n", "a=1/d\n", "A=[[1-a,a,0,0],[0,1-a,a,0],[0,0,1-a,a]]\n", "mu=[np.average(X[0:d],axis=0),np.average(X[d:2*d],axis=0),np.average(X[2*d:T],axis=0)]\n", "Sigma=[np.cov(X[0:d],rowvar=False)+0.2*np.identity(12),np.cov(X[d:2*d],rowvar=False)+0.2*np.identity(12),np.cov(X[2*d:T],rowvar=False)+0.2*np.identity(12)]\n", "plt.figure(figsize=(15,5))\n", "plt.subplot(211)\n", "plt.plot(np.transpose(mu))\n", "plt.legend(['state 0','state 1','state 2'])\n", "plt.title('Initial estimated HMM means')\n", "plt.subplot(212)\n", "plt.plot(np.transpose([ np.diag(S) for S in Sigma ]))\n", "plt.title('Initial estimated HMM variances')\n", "plt.xlabel('Feature dimension')" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "Now we'll compute the forward-backward algorithm using these initial estimates. First we compute B, a matrix whose $(i,t)^{\\textrm{th}}$ element is $p(\\vec{x}_t|q_t=i)$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### E-step part 1\n", "$$b_i(\\vec{x}_t)=p(\\vec{x}_t|q_t=i)=\\frac{1}{(2\\pi)^{D/2}|\\Sigma_i|^{1/2}}e^{-\\frac{1}{2}(\\vec{x}_t-\\vec\\mu_{i})^T\\Sigma_i^{-1}(\\vec{x}_t-\\vec\\mu_i)}$$\n", "For diagonal covariance Gaussians, that's\n", "$$b_i(\\vec{x}_t)=\\prod_{d=1}^{12} \\frac{1}{\\sqrt{2\\pi\\sigma_i^2}}e^{-\\frac{1}{2}\\left(\\frac{x_{dt}-\\mu_{di}}{\\sigma_i}\\right)^2}$$\n", "Actually, I'm not sure whether full-covariance or diagonal-covariance Gaussians give better results for this assignment. Full-covariance is a more accurate model, but it sometimes over-trains." ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0,0.5,'State number')" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "B=np.zeros((N,T))\n", "for t in range(0,T):\n", " for i in range(0,N):\n", " B[i,t]=stats.multivariate_normal(mu[i],Sigma[i]).pdf(X[t])\n", "plt.figure(figsize=(15,5))\n", "plt.imshow(np.log(B))\n", "plt.title('Log probability of the observation given the state')\n", "plt.xlabel('Frame number')\n", "plt.ylabel('State number')\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "### E-Step part 2\n", "Now we compute alpha, beta, gamma, and xi.\n", "$$\\alpha_0(i)=\\Pr\\left\\{q_0=i,\\vec{x}_0\\right\\}=\\pi_i b_i(\\vec{x}_0)$$\n", "$$\\alpha_t(i)=\\Pr\\left\\{q_t=i,\\vec{x}_0,\\ldots,\\vec{x}_t\\right\\}=b_i(\\vec{x}_t)\\sum_{j=0}^{N-1}\\alpha_{t-1}(j)a_{ji}$$\n", "$$\\beta_{T-1}(i)=1$$\n", "$$\\beta_{t}(i)=\\Pr\\left\\{\\vec{x}_{t+1},\\ldots,\\vec{x}_{T-1}|q_t=i\\right\\}\\sum_{j=0}^{N-1}a_{ij}b_j(\\vec{x}_{t+1})\\beta_{t+1}(j)$$\n", "$$\\gamma_t(i)=\\Pr\\left\\{q_t=i|\\vec{x}_0,\\ldots,\\vec{x}_{T-1}\\right\\}=\\frac{\\alpha_t(i)\\beta_t(i)}{\\sum_{j=0}^{N-1}\\alpha_t(j)\\beta_t(j)}$$\n", "$$\\xi_t(i,j)=\\Pr\\left\\{q_t=i,q_{t+1}=j|\\vec{x}_0,\\ldots,\\vec{x}_{T-1}\\right\\}=\\frac{\\alpha_t(i)a_{ij}b_j(\\vec{x}_{t+1})\\beta_{t+1}(j)}{\\sum_{i=0}^{N-1}\\sum_{j=0}^{N-1}\\alpha_t(i)a_{ij}b_j(\\vec{x}_{t+1})\\beta_{t+1}(j)}$$\n", "\n", "Notice that, since $a_{ij}=0$ except for $j\\in\\left\\{i,i+1\\right\\}$, therefore $\\xi_t(i,j)=0$ except for $j\\in\\left\\{i,i+1\\right\\}$. Therefore we can save a little space in computations by computing $\\xi_t(i,j)$ only for those two possibilities." ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:32: RuntimeWarning: divide by zero encountered in log\n" ] }, { "data": { "text/plain": [ "Text(0.5,0,'Frame index, t')" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "alpha = np.zeros((N,T))\n", "beta = np.zeros((N,T))\n", "gamma = np.zeros((N,T))\n", "xi = np.zeros((2*N,T))\n", "Amat = np.array(A) # Convert to an np matrix so we can compute inner products\n", "for i in range(0,N):\n", " alpha[i,0]=pi[i]*B[i,0]\n", "for t in range(1,T):\n", " for i in range(0,N):\n", " alpha[i,t]=B[i,t]*np.inner(alpha[:,t-1],Amat[:,i])\n", "for i in range(0,N):\n", " beta[i,T-1]=1\n", "for t in range(T-2,-1,-1):\n", " for i in range(0,N):\n", " beta[i,t]=np.inner(Amat[i,0:N],beta[:,t+1]*B[:,t+1])\n", "for t in range(0,T):\n", " gamma[:,t]=alpha[:,t]*beta[:,t]\n", " gamma[:,t]=gamma[:,t]/np.sum(gamma[:,t])\n", "for t in range(0,T):\n", " for i in range(0,N):\n", " for j in range(i,i+2):\n", " xi[i+j,t]=alpha[i,t]*Amat[i,j]\n", " if (t0','0->1','1->1','1->2','2->2','2->3'])\n", "plt.title('Xi')\n", "plt.xlabel('Frame index, t')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### M-Step for multiple files\n", "If you have multiple files, then you compute for example $\\gamma_{t\\ell}(i)$ for the $t^{th}$ frame of the $\\ell^{th}$ file\n", "$$a_{ij}=\\frac{\\sum_\\ell\\sum_t \\xi_{t\\ell}(i,j)}{\\sum_\\ell\\sum_t\\gamma_{t\\ell}(i)}\\approx \\Pr\\left\\{q_{t+1}=j|q_t=i\\right\\}$$\n", "$$\\vec\\mu_i=\\frac{\\sum_\\ell\\sum_t\\gamma_{t\\ell}(i)\\vec{x}_t}{\\sum_\\ell\\sum_t\\gamma_{t\\ell}(i)}\\approx E\\left[\\vec{x}_{t}|q_t=i\\right]$$\n", "$$\\sigma_{di}^2=\\frac{\\sum_\\ell\\sum_t\\gamma_{t\\ell}(i)(x_{dt}-\\mu_{di})^2}{\\sum_\\ell\\sum_t\\gamma_{t\\ell}(i)}\\approx E\\left[(x_{dt}-\\mu_{di})^2|q_t=i\\right]$$" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5,0,'Feature Dimension')" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for i in range(0,N):\n", " for j in range(i,i+2):\n", " A[i][j]=np.sum(xi[i+j,:])/np.sum(gamma[i,:])\n", "for i in range(0,N):\n", " mu[i] = np.inner(np.transpose(X),gamma[i,:])/np.sum(gamma[i,:])\n", "for i in range(0,N):\n", " Sigma[i]=0.2*np.identity(12)\n", " for t in range(0,len(X)):\n", " Sigma[i] += gamma[i,t]*np.outer(X[t]-mu[i],X[t]-mu[i])\n", "plt.figure(figsize=(15,5))\n", "plt.subplot(311)\n", "plt.plot(np.transpose(A))\n", "plt.title('Re-estimated Transition Probabilities')\n", "plt.subplot(312)\n", "plt.plot(np.transpose(mu))\n", "plt.title('Re-estimated Gaussian Means')\n", "plt.legend(['state 0','state 1','state 2'])\n", "plt.subplot(313)\n", "plt.plot(np.transpose([np.diag(S) for S in Sigma]))\n", "plt.title('Re-estimated Gaussian Variances')\n", "plt.xlabel('Feature Dimension')" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "### Iterating the EM algorithm\n", "In real life, we would iterate the above algorithm several times between the E-step and the M-step. We won't do that today." ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "# Scaled EM\n", "You might have noticed that $\\alpha_t(i)$ keeps getting smaller and smaller as you go further to the right. That's because the Gaussian pdf can be either bigger or smaller than 1.0, but usually it's much smaller.\n", "\n", "Suppose that $b_j(\\vec{x}_t)$ is typically around $0.001$. Then $\\alpha_t(i)\\sim 10^{-3t}\\sim 2^{-30t}$. Standard IEEE double-precision floating point can represent numbers as small as $2^{-1022}$, which means that you can compute the forward-backward algorithm for an audio file of at most $T\\le 1022/30=34$ frames. The problem is much worse on fixed-point embedded processors (obviously).\n", "\n", "The solution is to scale $\\alpha_t(i)$ and $\\beta_t(i)$. As long as we scale them by the same amount, then we can compute $\\gamma_t(i)$ without any special re-normalizing. It works like this:\n", "$$\\tilde{\\alpha}_t(i)=\\frac{\\alpha_t(i)}{\\prod_{\\tau=1}^t g_\\tau}$$\n", "$$\\tilde{\\beta}_t(i)=\\frac{\\beta_t(i)}{\\prod_{\\tau=t+1}^T g_\\tau}$$\n", "$$\\gamma_t(i)=\\frac{\\alpha_t(i)\\beta_t(i)}{\\sum_{j=0}^{N-1}\\alpha_t(j)\\beta_t(j)}$$\n", "$$=\\frac{\\frac{\\alpha_t(i)\\beta_t(i)}{\\prod_{\\tau=1}^T g_\\tau}}{\\frac{\\sum_{j=0}^{N-1}\\alpha_t(j)\\beta_t(j)}{\\prod_{\\tau=1}^T g_\\tau}}$$\n", "$$=\\frac{\\tilde{\\alpha}_t(i)\\tilde{\\beta}_t(i)}{\\sum_{j=0}^{N-1}\\tilde{\\alpha}_t(j)\\tilde{\\beta}_t(j)}$$\n", "\n", "So any scaling constant $g_t$ will work, AS LONG AS YOU USE THE SAME $g_t$ FOR BOTH ALPHA AND BETA!!!\n", "\n", "Here's a pretty reasonable choice:\n", "$$\\bar\\alpha_t(i)=b_i(\\vec{x}_t)\\sum_{j=0}^{N-1}\\tilde{\\alpha}_{t-1}(j)a_{ji}$$\n", "$$g_t=\\sum_{i=0}^{N-1}\\bar\\alpha_t(i)$$\n", "$$\\tilde\\alpha_t(i) = \\frac{1}{g_t}\\bar\\alpha_t(i)$$\n", "\n", "If you work through it, you discover that, with this choice,\n", "$$\\prod_{t=1}^T g_t = \\sum_{j=0}^{N-1}\\alpha_T(j)$$\n", "\n", "But you might remember that $\\sum_{j=0}^{N-1}\\alpha_T(j)$ is actually the probability of the data sequence, $X$, given the model parameters $\\Lambda$. So\n", "$$p(X|\\Lambda)=\\sum_{j=0}^{N-1}\\alpha_T(j)=\\prod_{t=1}^T g_t$$\n", "$$\\ln p(X|\\Lambda)=\\sum_{t=1}^{T}\\ln g_t$$\n", "\n", "So we don't need to store $g_t$, just $\\ln g_t$." ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5,0,'Frame Index')" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tildealpha=np.zeros((N,T))\n", "tildebeta=np.zeros((N,T))\n", "log_g = np.zeros((T))\n", "baralpha = np.zeros((N,T))\n", "Amat = np.array(A)\n", "\n", "for i in range(0,N):\n", " baralpha[i,0]=pi[i]*B[i,0]\n", "log_g[0] = np.log(np.sum(baralpha[:,0]))\n", "tildealpha[:,0]=baralpha[:,0]/np.exp(log_g[0])\n", "\n", "for t in range(1,T):\n", " for i in range(0,N):\n", " baralpha[i,t]=B[i,t]*np.inner(tildealpha[:,t-1],Amat[:,i])\n", " log_g[t] = np.log(np.sum(baralpha[:,t]))\n", " tildealpha[:,t]=baralpha[:,t]/np.exp(log_g[t])\n", "\n", "for i in range(0,N):\n", " tildebeta[i,T-1] = 1/np.exp(log_g[T-1])\n", "\n", "for t in range(T-2,-1,-1):\n", " for i in range(0,N):\n", " tildebeta[i,t]=np.inner(Amat[i,0:N],tildebeta[:,t+1]*B[:,t+1])/np.exp(log_g[t+1])\n", "\n", "for t in range(0,T):\n", " gamma[:,t] = tildealpha[:,t]*tildebeta[:,t]\n", " gamma[:,t] = gamma[:,t]/np.sum(gamma[:,t])\n", " \n", "plt.figure(figsize=(15,5))\n", "plt.subplot(311)\n", "plt.plot(log_g)\n", "plt.title('Log Gain at each Frame')\n", "plt.subplot(312)\n", "plt.plot(np.transpose(tildealpha))\n", "plt.title('Tilde-Alpha')\n", "plt.legend(['state 0','state 1','state 2'])\n", "plt.subplot(313)\n", "plt.plot(np.transpose(gamma))\n", "plt.title('Gamma')\n", "plt.xlabel('Frame Index')\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "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": "3.6.4" } }, "nbformat": 4, "nbformat_minor": 2 }