MAP Estimation for General Conditional Gaussian Distributions

• Activity Number: 52
• Type: Contributed
• Date/Time: Sunday, August 11, 2002 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Computing*
• Author(s): Christopher Raphael*+
• Affiliation(s): University of Massachusetts
• Keywords: conditional Gaussian distribution ; MAP estimate ; dynamic programming ; rhythmic parsing ; graphical models

Abstract

A conditional Gaussian (CG) distribution models a mixture of discrete and continuous variables in which, for each configuration of the discrete variables, the continuous variables have a multivariate Gaussian distribution. We present methodology for computing the globally most likely configuration of unobserved variables, given observed variables of a CG distribution. We represent the CG distribution, using ideas from graphical models, as a product of potentials over cliques in a junction tree. In this setting, we perform dynamic programming by representing the probability of the most likely configuration of each subtree in a form that is closed under the dynamic programming recursion. A "thinning" algorithm keeps the complexity of the representation computationally manageable, without involving approximation. We demonstrate an application to simultaneous estimation of time-varying tempo and rhythm, given musical performance data. In this application we estimate the MAP configuration of several thousand variables.