عنوان

Variational Bayesian learning theory /

(Number (ISBN

1107430763

(Number (ISBN

1139879359

(Number (ISBN

1316998312

(Number (ISBN

9781107430761

(Number (ISBN

9781139879354

(Number (ISBN

9781316998311

Erroneous ISBN

1107076153

Erroneous ISBN

9781107076150

Erroneous ISBN

9781107430761

Title Proper

Variational Bayesian learning theory /

General Material Designation

[Book]

First Statement of Responsibility

Shinichi Nakajima, Kazuho Watanabe, Masashi Sugiyama.

Place of Publication, Distribution, etc.

Cambridge :

Name of Publisher, Distributor, etc.

Cambridge University Press,

Date of Publication, Distribution, etc.

2019.

Specific Material Designation and Extent of Item

1 online resource (xv, 543 pages)

Text of Note

Title from publisher's bibliographic system (viewed on 28 Jun 2019).

Text of Note

Includes bibliographical references and indexes.

Text of Note

Cover; Half-title; Title page; Copyright information; Contents; Preface; Nomenclature; Part I Formulation; 1 Bayesian Learning; 1.1 Framework; 1.1.1 Bayes Theorem and Bayes Posterior; 1.1.2 Maximum A Posteriori Learning; 1.1.3 Bayesian Learning; 1.1.4 Latent Variables; 1.1.5 Empirical Bayesian Learning; 1.2 Computation; 1.2.1 Popular Distributions; 1.2.2 Conjugacy; 1.2.3 Posterior Distribution; 1.2.4 Posterior Mean and Covariance; 1.2.5 Predictive Distribution; 1.2.6 Marginal Likelihood; 1.2.7 Empirical Bayesian Learning; 2 Variational Bayesian Learning; 2.1 Framework

Text of Note

2.1.1 Free Energy Minimization2.1.2 Conditional Conjugacy; 2.1.3 Constraint Design; 2.1.4 Calculus of Variations; 2.1.5 Variational Bayesian Learning; 2.1.6 Empirical Variational Bayesian Learning; 2.1.7 Techniques for Nonconjugate Models; 2.2 Other Approximation Methods; 2.2.1 Laplace Approximation; 2.2.2 Partially Bayesian Learning; 2.2.3 Expectation Propagation; 2.2.4 Metropolis-Hastings Sampling; 2.2.5 Gibbs Sampling; Part II Algorithm; 3 VB Algorithm for Multilinear Models; 3.1 Matrix Factorization; 3.1.1 VB Learning for MF; 3.1.2 Special Cases

Text of Note

3.2 Matrix Factorization with Missing Entries3.2.1 VB Learning for MF with Missing Entries; 3.3 Tensor Factorization; 3.3.1 Tucker Factorization; 3.3.2 VB Learning for TF; 3.4 Low-Rank Subspace Clustering; 3.4.1 Subspace Clustering Methods; 3.4.2 VB Learning for LRSC; 3.5 Sparse Additive Matrix Factorization; 3.5.1 Robust PCA and Matrix Factorization; 3.5.2 Sparse Matrix Factorization Terms; 3.5.3 Examples of SMF Terms; 3.5.4 VB Learning for SAMF; 4 VB Algorithm for Latent Variable Models; 4.1 Finite Mixture Models; 4.1.1 Mixture of Gaussians; 4.1.2 Mixture of Exponential Families

Text of Note

4.1.3 Infinite Mixture Models4.2 Other Latent Variable Models; 4.2.1 Bayesian Networks; 4.2.2 Hidden Markov Models; 4.2.3 Probabilistic Context-Free Grammars; 4.2.4 Latent Dirichlet Allocation; 5 VB Algorithm under No Conjugacy; 5.1 Logistic Regression; 5.2 Sparsity-Inducing Prior; 5.3 Unified Approach by Local VB Bounds; 5.3.1 Divergence Measures in LVA; 5.3.2 Optimization of Approximations; 5.3.3 An Alternative View of VB for Latent Variable Models; Part III Nonasymptotic Theory; 6 Global VB Solution of Fully Observed Matrix Factorization; 6.1 Problem Description

Text of Note

6.2 Conditions for VB Solutions6.3 Irrelevant Degrees of Freedom; 6.4 Proof of Theorem 6.4; 6.4.1 Proof for Case 1; 6.4.2 Proof for Case 2; 6.4.3 Proof for Case 3; 6.4.4 General Expression; 6.5 Problem Decomposition; 6.6 Analytic Form of Global VB Solution; 6.7 Proofs of Theorem 6.7 and Corollary 6.8; 6.7.1 Null Stationary Point; 6.7.2 Positive Stationary Point; 6.7.3 Useful Relations; 6.7.4 Free Energy Comparison; 6.8 Analytic Form of Global Empirical VB Solution; 6.9 Proof of Theorem 6.13; 6.9.1 EVB Shrinkage Estimator; 6.9.2 EVB Threshold; 6.10 Summary of Intermediate Results

0

8

8

8

8

Text of Note

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.

International Standard Book Number

9781107076150

Bayesian field theory.

Probabilities.

Bayesian field theory.

Probabilities.

Number

Edition

Class number

Book number

Nakajima, Shin'ichi

Sugiyama, Masashi,1974-

Watanabe, Kazuho

Date of Transaction

20200822145813.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y