Variational Bayesian Learning Theory


Variational Bayesian Learning Theory
Authors:Shinichi Nakajima – Kazuho Watanabe – Masashi Sugiyama
ISBN-10 书号:1107076153
ISBN-13 书号:9781107076150
Edition 版次:1
Release Finelybook 出版日期:2019-08-22
pages 页数:558 pages


Book Description
Variational Bayesian learning is one of the most popular methods in machine learning. Designed for researchers and graduate students in machine learning, this book summarizes recent developments in the non-asymptotic and asymptotic theory of variational Bayesian learning and suggests how this theory can be applied in practice. The authors begin by developing a basic framework with a focus on conjugacy, which enables the reader to derive tractable algorithms. Next, it summarizes non-asymptotic theory, which, although limited in application to bilinear models, precisely describes the behavior of the variational Bayesian solution and reveals its sparsity inducing mechanism. Finally, the text summarizes asymptotic theory, which reveals phase transition phenomena depending on the prior setting, thus providing suggestions on how to set hyperparameters for particular purposes. Detailed derivations allow readers to follow along without prior knowledge of the mathematical techniques specific to Bayesian learning.

Contents
Preface
Nomenclature
Part I Formulation
1Bayesian Learning
2Variational Bayesian Learning
Part ll Algorithm
3 VB Algorithm for Multilinear Models
4VB Algorithm for Latent Variable Models
5 VB Algorithm under No Conjugacy
Part ll Nonasymptotic Theory
6 Global VB Solution of Fully ObservedMatrix Factorization
7 Model-Induced Regularization and Sparsitylnducing Mechanism
8 Performance Analysis of VB MatrixFactorization
9 Global Solver for Matrix Factorization
10 Global Solver for Low-RankSubspace Clustering
11 Efficient Solver for Sparse AdditiveMatrix Factorization
12MAP and Partially Bayesian Learning
Part IV Asymptotic Theory
13 Asymptotic Learning Theory
14 Asymptotic VB Theory of ReducedRank Regression
15Asymptotic VB Theory of Mixture Models
16Asymptotic VB Theory of Other LatentVariable Models
17 Unified Theory for Latent Variable Models
Appendix A James-Stein Estimator
Appendix B Metric in Parameter Space
Appendix C Detailed Descriptionof Overlap Method
Appendix D Optimality of Bayesian Learning
Bibliography
Subject Index


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