Title: Bayesian structure learning in high-dimensional graphical models with application to brain connectivity
Authors: Reza Mohammadi - University of Amsterdam (Netherlands) [presenting]
Helene Massam - York University (Canada)
Abstract: The problem of Bayesian structure learning in high-dimensional graphical models is considered, motivated by brain connectivity applications. In graphical models, Bayesian frameworks provide a straightforward tool, explicitly incorporating underlying graph uncertainty. In principle, the Bayesian approaches are based on averaging the posterior distributions of the quantity of interest, weighted by their posterior graph probabilities. However, Bayesian inference has not been used in practice for high-dimensional graphical models, because computing the posterior graph probabilities is hard and the number of possible graph models is very large. We discuss the computational problems related to Bayesian structure learning and we offer several solutions to cope the high-dimensionality problems. We apply our method to high-dimensional fMRI data from brain connectivity studies to show its empirical usefulness. In addition, we have implemented our method in the R package BDgraph which is available online.