{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "*A live version of this Jupyter R notebook can be downloaded from http://cs.jhu.edu/~jason/tutorials/GMM-optimization.ipynb*.\n", "\n", "# Dynamics of optimizing Gaussian mixture models\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This super-simple example illustrates how a Gaussian mixture model behaves with high and low fixed variance (that is, how it collapses or specializes the clusters as in deterministic annealing).\n", "\n", "We then examine what happens when we try to _optimize_ the variance together with the means. \n", "\n", "* **Good news:** It's optimal to _specialize_ into low-variance clusters, as expected, and EM or gradient descent will eventually discover this. \n", "\n", "* **Bad news:** Many optimization algorithms are attracted into the neighborhood of a bad saddle point. They then spend most of their time hanging out there before eventually finding the right solution. Or worse, they stop numerically near the saddle point before they get to the right solution.\n", "\n", " This bad saddle point is a symmetric solution with high variance. The clusters _collapse_ into a single cluster whose variance matches the sample variance. \n", "\n", "* **Recommendation:** Thus, rather than using the gradient to optimize the variance, it really is a good idea to sweep through different variance values as an outer loop around the optimizer. This actively pushes the system away from the saddle point.\n", "\n", " Deterministic annealing (DA) does this. Often DA is sold as a way to (hopefully) escape bad local optima in latent-variable models. But it may also be useful in general for escaping the saddle points of such models, which may not be terminal points for optimization but can greatly slow it down. This super-simple example has no bad local optima, just saddle points." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Model and log-likelihood function\n", "Throughout the investigation, our model is an equal mixture of two univariate Gaussians with \n", "symmetric means $\\mu,-\\mu$ and common variance $\\sigma^2$ with $\\sigma > 0$. The log-density of the mixture is" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# addition in the log domain to avoid underflow.\n", "# This version can add two vectors in parallel.\n", "logadd <- function (a,b) { ifelse(a==-Inf, b, # The ifelse test avoids the problem that -Inf minus -Inf NaN.\n", " pmax(a,b) + log1p(exp(pmin(a,b)-pmax(a,b)))) } " ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# mixture of univariate Gaussians\n", "ldmix <- function (x,mu,sigma) {\n", " sigma <- pmax(0,sigma) # since an unbounded optimizer might explore sigma < 0, just treat that like 0\n", " # Loses precision:\n", " # log((dnorm(x,mu,pmax(0,sigma))+dnorm(x,-mu,pmax(0,sigma)))/2)\n", " logadd( dnorm(x,mu,sigma,log=T) , dnorm(x,-mu,sigma,log=T) ) - log(2)\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We'll also assume that the only observed datapoints are at 1 and -1. Then the log-likelihood is" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "ll <- function (mu,sigma) ldmix(1,mu,sigma)+ldmix(-1,mu,sigma)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Let's visualize that log-likelihood function:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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quJSfjup7LLGMFuyuLrvluTkHANo7sKKd0M77yT+c0mtXNojdKvt8EWfNFdK8a1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\nBJWX/YO8mX8qCMAmsp4za5Il9W4VJvgBNPSTiYs7IodNpR9aOIg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d+KjSHbZ+D/DpOdU4F7GqXn+diutU3RolE2LjlrD3t9ta1gYr2d5N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ZgiM4dZx6yfNec1JhrXZ92/K4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\nRf9cj/sI6c0oK/9XzqX4tFjh3L6on5/AgweVvmGug9O+F2LtwaIWBfNg5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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mu <- seq(-2,2,length.out=50)\n", "sigma <- seq(0.5,2,length.out=50)\n", "log_lik <- outer(mu,sigma,Vectorize(ll))\n", "persp(mu, sigma, log_lik, theta=30, phi=30, ticktype=\"detailed\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "At each fixed $\\sigma$:\n", "* The symmetry in $\\mu$ comes from the fact that we can swap the clusters and get the same likelihood.\n", "* There is an extremum at $\\mu=0$,\n", " * which is a _local minimum_ for $\\sigma < 1$ (so the clusters like to move apart)\n", " * but a _global maximum_ for $\\sigma \\geq 1$ (where the clusters like to move together).\n", " * These correspond to low and high temperature in deterministic annealing.\n", " * The phase shift happens at the \"critical temperature\" where $\\sigma = 1$, probably because that's the _sample_ stdev.\n", " \n", "We can see that transition by zooming in on $\\sigma \\approx 1$:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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W9TXMGk9zQLcGeNpuBcg5T0g4kYh/3SC7xu6pPElr8UjOVs/JAEeuBPRf76H81M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HabiLEpKKqvjzl5NIZdgDm9HSByB0wUx2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\n/65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7I6jMZS7BAvnkO53zJDErNLCJeq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\ni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HnuQX1hhYSI6MdCEhpkc4xf9e/kWv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\nITGMBP4fyZd63Fcbs+sAAAAASUVORK5CYII=", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sigma <- seq(0.9,1.1,length.out=50)\n", "log_lik <- outer(mu,sigma,Vectorize(ll))\n", "persp(mu, sigma, log_lik, theta=30, phi=30, ticktype=\"detailed\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we allow $\\sigma$ to vary, however:\n", "\n", "* The global maximum puts one cluster at each point, with $\\sigma$ as small as possible. (Actually there are two symmetric maxima of this sort.)\n", "* So $\\sigma$ _wants_ to become small, allowing the clusters to specialize." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Alternating optimization\n", "\n", "But when can we computationally find this maximum? There are are no other local maxima on the whole surface. But finding a global maximum might still be hard! The problem is that $(\\mu=0,\\sigma=1)$ is a very stable and somewhat attractive saddle point.\n", "\n", "Let's see what goes wrong in the case of alternating optimization.\n", "\n", "First we hold $\\sigma > 1$ fixed while optimizing $\\mu$. The argmax is $\\mu=0$ (the Gaussian mixture becomes a single Gaussian):" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "library(repr)\n", "options(repr.plot.width=3, repr.plot.height=3) # smaller plots" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(function (mu) ll(mu,1.1), xlab=\"mu\", xlim=c(-2,2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we hold $\\mu=0$ fixed while optimizing $\\sigma$. It moves to the sample stdev, namely 1. (In fact, this is true regardless of where $\\sigma$ starts.)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(function (sigma) ll(0,sigma), xlab=\"sigma\", xlim=c(0.5, 2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We're now stuck at this saddle point $(\\mu,\\sigma)=(0,1)$: for this $\\sigma$, our current $\\mu=0$ is already optimal. " ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(function (mu) ll(mu,1), xlab=\"mu\", xlim=c(-2,2))\n", "plot(function (mu) ll(mu,1), xlim=c(-.01,.01)) # zooming in" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# The Hessian\n", "Pause for a moment to notice how flat the top of that graph is. Not only is this a critical point, but the Hessian is singular, so if we start near the critical point, even a second-order optimizer will be slow to get away. The Hessian is $\\left( \\begin{array}{cc}\\frac{\\partial^2}{\\partial^2\\mu} & \\frac{\\partial^2}{\\partial\\sigma\\partial\\mu} \\\\ \\frac{\\partial^2}{\\partial\\mu\\partial\\sigma} & \\frac{\\partial^2}{\\partial^2\\sigma}\\end{array} \\right)L = \\left( \\begin{array}{rr}0 & 0 \\\\ 0 & -4\\end{array} \\right)$:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
-1.049523e-08 | -2.64677e-09 |
-2.646770e-09 | -4.00000e+00 |