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.
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.
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