[Lisa_seminaires] Kevin Murphy @ McGill on Friday

Dumitru Erhan dumitru.erhan at umontreal.ca
Mar 24 Mar 16:33:29 EDT 2009


Title: Computationally and statistically efficient methods for model
selection in graphical models

Speaker: Kevin Murphy (Stats/CS, U. British Columbia)

Time/Place: Friday, 11am in Macdonald-Harrington G-01

Abstract:

Graphical models are a way of representing conditional independence
relationships between random variables using graphs. In this talk, we
discuss ways of learning the structure of graphs from data. This is
useful for visualizing relationships between variables in
high-dimensional data, as well as for building density models for use in
prediction, classification, clustering, etc. We will focus on undirected
graphs (also called random fields), and in particular on methods based
on L1-penalized maximum likelihood. First we extend existing results for
the Gaussian and binary case to the more general case of conditional
random fields and multi-state models. This requires that we replace the
L1 penalty with a group L1 penalty, which poses various computational
challenges. The second extension is to estimate the group structure (by
clustering the variables) while simultaneously learning the graph
structure. This technique relies on new bounds on the partition function
for the positive definite matrix Laplace distribution, which also has
applications in hierarchical Bayesian analysis of multiple related graphs.


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