Graphical Models, Exponential Families, and Variational Inference

Martin J. Wainwright, Michael I. Jordan (Autoren)

Buch | Softcover

324 Seiten

2008
now publishers Inc (Verlag)
978-1-60198-184-4 (ISBN)

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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, this book 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.

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

Erscheint lt. Verlag	15.12.2008
Reihe/Serie	Foundations and Trends® in Machine Learning
Verlagsort	Hanover
Sprache	englisch
Maße	156 x 234 mm
Gewicht	457 g
Themenwelt	Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik
ISBN-10	1-60198-184-8 / 1601981848
ISBN-13	978-1-60198-184-4 / 9781601981844
Zustand	Neuware