Variational Bayesian Learning Theory

Shinichi Nakajima (Technische Universität Berlin), Kazuho Watanabe, Masashi Sugiyama (University of Tokyo)

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English

Cambridge University Press
11 July 2019

Science: general issues; Machine learning

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.

By: Shinichi Nakajima (Technische Universität Berlin), Kazuho Watanabe, Masashi Sugiyama (University of Tokyo)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 235mm, Width: 156mm, Spine: 34mm
Weight: 900g
ISBN: 9781107076150
ISBN 10: 1107076153
Pages: 558
Publication Date: 11 July 2019
Audience: College/higher education , Professional and scholarly , Further / Higher Education , Undergraduate
Format: Hardback
Publisher's Status: Active

1. Bayesian learning; 2. Variational Bayesian learning; 3. VB algorithm for multi-linear models; 4. VB Algorithm for latent variable models; 5. VB algorithm under No Conjugacy; 6. Global VB solution of fully observed matrix factorization; 7. Model-induced regularization and sparsity inducing mechanism; 8. Performance analysis of VB matrix factorization; 9. Global solver for matrix factorization; 10. Global solver for low-rank subspace clustering; 11. Efficient solver for sparse additive matrix factorization; 12. MAP and partially Bayesian learning; 13. Asymptotic Bayesian learning theory; 14. Asymptotic VB theory of reduced rank regression; 15. Asymptotic VB theory of mixture models; 16. Asymptotic VB theory of other latent variable models; 17. Unified theory.

Shinichi Nakajima is a senior researcher at Technische Universität Berlin. His research interests include the theory and applications of machine learning, and he has published papers at numerous conferences and in journals such as the Journal of Machine Learning Research, the Machine Learning Journal, Neural Computation, and IEEE Transactions on Signal Processing. He currently serves as an area chair for NIPS and an action Editor for Digital Signal Processing. Kazuho Watanabe is a lecturer at Toyohashi University of Technology. His research interests include statistical machine learning and information theory, and he has published papers at numerous conferences and in journals such as the Journal of Machine Learning Research, the Machine Learning Journal, IEEE Transactions on Information Theory, and IEEE Transactions on Neural Networks and Learning Systems. Masashi Sugiyama is Director of the RIKEN Center for Advanced Intelligence Project and Professor of Complexity Science and Engineering at the University of Tokyo. His research interests include the theory, algorithms, and applications of machine learning. He has written several books on machine learning, including Density Ratio Estimation in Machine Learning (Cambridge, 2012). He served as program co-chair and general co-chair of the NIPS conference in 2015 and 2016, respectively, and received the Japan Academy Medal in 2017.

Reviews for Variational Bayesian Learning Theory

'This book is an excellent and comprehensive reference on the topic of Variational Bayes (VB) inference, which is heavily used in probabilistic machine learning. It covers VB theory and algorithms, and gives a detailed exploration of these methods for matrix factorization and extensions. It will be an essential guide for those using and developing VB methods.' Chris Williams, University of Edinburgh 'This book presents a very thorough and useful explanation of classical (pre deep learning) mean field variational Bayes. It covers basic algorithms, detailed derivations for various models (eg matrix factorization, GLMs, GMMs, HMMs), and advanced theory, including results on sparsity of the VB estimator, and asymptotic properties (generalization bounds).' Kevin Murphy, Research scientist, Google Brain