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If you're curious about the process that went into writing my book,I did an interview with Computer Vision News (March 2022).First editionYou can still download the first edition orpotentially purchase it online.The first edition is also available in Chineseand Japanese(translated by Prof. Toru Tamaki).
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Chapter 1 presents background material on Bayesian inference,graphical models, and propagation algorithms. Chapter 2 forms thetheoretical core of the thesis, generalising theexpectation-maximisation (EM) algorithm for learning maximumlikelihood parameters to the VB EM algorithm which integrates overmodel parameters. The algorithm is then specialised to the largefamily of conjugate-exponential (CE) graphical models, and severaltheorems are presented to pave the road for automated VB derivationprocedures in both directed and undirected graphs (Bayesian and Markovnetworks, respectively).
Chapters 3-5 derive and apply the VB EM algorithm to threecommonly-used and important models: mixtures of factor analysers,linear dynamical systems, and hidden Markov models. It is shown howmodel selection tasks such as determining the dimensionality,cardinality, or number of variables are possible using VBapproximations. Also explored are methods for combining samplingprocedures with variational approximations, to estimate the tightnessof VB bounds and to obtain more effective sampling algorithms.Chapter 6 applies VB learning to a long-standing problem of scoringdiscrete-variable directed acyclic graphs, and compares theperformance to annealed importance sampling amongst othermethods. Throughout, the VB approximation is compared to other methodsincluding sampling, Cheeseman-Stutz, and asymptotic approximationssuch as BIC. The thesis concludes with a discussion of evolvingdirections for model selection including infinite models andalternative approximations to the marginal likelihood. 041b061a72
