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.