Variational Bayesian Learning Theory
Published on 6. February 2025
Book
Paperback/Softback
559 pages
978-1-107-43076-1 (ISBN)
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.
Reviews / Votes
'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 '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 EdinburghMore details
Language
English
Place of publication
Cambridge
United Kingdom
Target group
College/higher education
Professional and scholarly
Product notice
Paperback (trade)
Dimensions
Height: 229 mm
Width: 152 mm
Thickness: 33 mm
Weight
898 gr
ISBN-13
978-1-107-43076-1 (9781107430761)
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Schweitzer Classification
Other editions
Additional editions
Shinichi Nakajima | Kazuho Watanabe | Masashi Sugiyama
Variational Bayesian Learning Theory
Book
07/2019
Cambridge University Press
€164.10
Shipment within 15-20 days
Persons
Shinichi Nakajima is a senior researcher at Technische Universitaet 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.
Content
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.