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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, 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.
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