Variational algorithms for approximate Bayesian inference (2003)
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@TECHREPORT{Beal03variationalalgorithms,
author = {Matthew J. Beal},
title = {Variational algorithms for approximate Bayesian inference},
institution = {},
year = {2003}
}
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Abstract
The Bayesian framework for machine learning allows for the incorporation of prior knowledge in a coherent way, avoids overfitting problems, and provides a principled basis for selecting between alternative models. Unfortunately the computations required are usually intractable. This thesis presents a unified variational Bayesian (VB) framework which approximates these computations in models with latent variables using a lower bound on the marginal likelihood. Chapter 1 presents background material on Bayesian inference, graphical models, and propaga-tion algorithms. Chapter 2 forms the theoretical core of the thesis, generalising the expectation-maximisation (EM) algorithm for learning maximum likelihood parameters to the VB EM al-gorithm which integrates over model parameters. The algorithm is then specialised to the large family of conjugate-exponential (CE) graphical models, and several theorems are presented to pave the road for automated VB derivation procedures in both directed and undirected graphs (Bayesian and Markov networks, respectively). Chapters 3-5 derive and apply the VB EM algorithm to three commonly-used and important models: mixtures of factor analysers, linear dynamical systems, and hidden Markov models.
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