Shinichi Nakajima, Kazuho Watanabe, Masashi SugiyamaCambridge University Press, 7/11/2019EAN 9781107076150, ISBN10: 1107076153Hardcover, 558 pages, 23.6 x 15.5 x 3.3 cmLanguage: EnglishVariational 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.1. Bayesian learning2. Variational Bayesian learning3. VB algorithm for multi-linear models4. VB Algorithm for latent variable models5. VB algorithm under No Conjugacy6. Global VB solution of fully observed matrix factorization7. Model-induced regularization and sparsity inducing mechanism8. Performance analysis of VB matrix factorization9. Global solver for matrix factorization10. Global solver for low-rank subspace clustering11. Efficient solver for sparse additive matrix factorization12. MAP and partially Bayesian learning13. Asymptotic Bayesian learning theory14. Asymptotic VB theory of reduced rank regression15. Asymptotic VB theory of mixture models16. Asymptotic VB theory of other latent variable models17. Unified theory.
