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Cited by 1,820

The DOI matches its Crossref record; 13 of the 13 references it cites were found in a registry or an index.

Graphical Models, Exponential Families, and Variational Inference

Wainwright, Martin J., Jordan, Michael I.·2008·Foundations and Trends® in Machine Learning
DOI 10.1561/2200000001
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Abstract

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, we develop general variational representations of the problems of computing likelihoods, marginal probabilities and most probable configurations. We describe how a wide variety of algorithms — among them sum-product, cluster variational methods, expectation-propagation, mean field methods, max-product and linear programming relaxation, as well as conic programming relaxations — 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.

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Metadata

Authors
Wainwright, M. J., & Jordan, M. I.
Venue
Foundations and Trends® in Machine Learning
Publisher
Emerald
Published
2008-12-18
Volume
1
Issue
1-2
Pages
1-305
ISSN
  • 1935-8237 (ISSN-L)
  • 1935-8245
DOI
10.1561/2200000001
OpenAlex
W4293052541
Cited by
1,820
References
13
FWCI
62.01
Type
journal article
Language
en
Open access
closed

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