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Variational Bayesian Learning Theory

$140.00

  • Date Published: July 2019
  • availability: Available
  • format: Hardback
  • isbn: 9781107076150

$ 140.00
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About the Authors
  • 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.

    • Provides a detailed theory of variational Bayesian learning and suggests various applications
    • Introduces and covers recent developments in non-asymptotic and asymptotic theory
    • The content is accessible to students without prior knowledge of techniques, featuring detailed derivations and explanations of new concepts
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    Reviews & endorsements

    '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 Edinburgh

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    Product details

    • Date Published: July 2019
    • format: Hardback
    • isbn: 9781107076150
    • length: 558 pages
    • dimensions: 235 x 156 x 34 mm
    • weight: 0.9kg
    • availability: Available
  • Table of Contents

    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.

  • Authors

    Shinichi Nakajima, Technische Universität Berlin
    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, Toyohashi University of Technology
    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, University of Tokyo
    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.

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