Variational Bayesian Learning Theory
Variational Bayesian Learning Theory by Shinichi Nakajima, published by Cambridge University Press on February 6, 2025, is a comprehensive resource for researchers and graduate students in the field of machine learning. This 559-page book provides an overview of variational Bayesian learning, a widely used method in the discipline, and summarizes both non-asymptotic and asymptotic theories while offering practical applications of these concepts.
Readers will find a structured approach that begins with a basic framework emphasizing conjugacy, which aids in deriving tractable algorithms. The book details non-asymptotic theory, focusing on its implications for bilinear models and the behavior of variational Bayesian solutions, including their sparsity-inducing mechanisms. Additionally, it explores asymptotic theory and its phase transition phenomena, providing insights on hyperparameter settings for various applications. The text is designed to be accessible, with detailed derivations that do not assume prior knowledge of the mathematical techniques specific to Bayesian learning.
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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.
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