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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENTAL SEMINAR}
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\centerline{4:15 p.m., Tuesday, February 17, 2004}
\centerline{Sequoia Hall Room 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl Martin Wainwright}
\centerline{\sl UC Berkeley}
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\centerline{\bf Graphical models, variational methods, and their applications}

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Abstract:

Graphical models are used and studied in a variety of
applied statistical and computational fields, including
bioinformatics, statistical physics, signal and image processing,
communication theory, and machine learning.  Many large-scale
inference problems that arise in specific instances, including the key
problems of computing likelihoods, marginals and modes associated with
probability distributions, are best studied in the general setting.

Variational methods provide a complementary alternative to Markov
chain Monte Carlo as a general source of approximation methods for
inference in large-scale statistical models.  Underlying a variety of
these methods (e.g., mean field, belief propagation) is a classical
variational principle from statistical physics, which involves a
``free energy'' optimization problem over the set of all
distributions.  We describe an alternative view, that exploits the
framework of exponential families and associated conjugate duality
relations, in which the optimization takes place over the (typically)
much lower-dimensional space of mean parameters.  This viewpoint
clarifies the essential ingredients of known variational techniques,
and also suggests novel methods based on convex relaxations.  We
discuss applications of graphical models and variational methods to
problems including natural image statistics, and decoding of
error-control codes.

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