
Graphical Models, Exponential Families, and Variational Inference
now publishers Inc
1st Edition
Published on 15. December 2008
Book
Paperback/Softback
324 pages
978-1-60198-184-4 (ISBN)
Description
The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building large-scale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances-including the key problems of computing marginals and modes of probability distributions-are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, Graphical Models, Exponential Families and Variational Inference develops general variational representations of the problems of computing likelihoods, marginal probabilities and most probable configurations. It describes how a wide variety of algorithms- among them sum-product, cluster variational methods, expectation-propagation, mean field methods, and max-product-can all be understood in terms of exact or approximate forms of these variational representations. The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in large-scale statistical models.
More details
Series
Language
English
Place of publication
Hanover
United States
Target group
Professional and scholarly
Dimensions
Height: 234 mm
Width: 156 mm
Thickness: 17 mm
Weight
457 gr
ISBN-13
978-1-60198-184-4 (9781601981844)
DOI
10.1561/2200000001
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Schweitzer Classification
Content
1: Introduction 2: Background 3: Graphical models as exponential families 4: Sum product, Bethe-Kikuchi, and expectation-propagation 5: Mean field methods 6: Variational methods in parameter estimation 7: Convex relaxations and upper bounds 8: Max-product and LP relaxations 9: Moment matrices and conic relaxations 10: Discussion. A: Background Material B: Proofs for exponential families and duality C: Variational principles for multivariate Gaussians D: Clustering and augmented hypergraphs E: Miscellaneous results References