Approximate Centroid Inference for Complex Graphical Models

• Activity Number: 174
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Hunter Glanz*+ and Luis Carvalho
• Companies: Boston University and Boston University
• Keywords: hierarchical model ; MCMC ; centroid estimation

Abstract

High dimensional, highly connected graphical models continue to receive an increasing amount of attention and use as a result of the voluminous datasets gathered by modern-day technology. Many traditional models tend to narrow their focus beyond the scale of interest, make unrealistic model assumptions or suffer from unreasonable computation times. In this talk we will discuss how we approximate an example of such complex graphical models -- a model that aims to classify node labels in a three-dimensional lattice -- with random spanning trees. In doing so, we reduce the computational complexity immensely while still preserving, on average, the meaning of the model. More precisely, we define a hierarchical prior distribution on the space of spanning trees of the original graph and then develop a Metropolis-within-Gibbs algorithm to sample from the posterior space. To further increase computational efficiency, we adopt a centroid tree estimate and conduct exact posterior inference of the node labels conditional on this spanning tree estimate, similar to an empirical Bayes approach.