Bayesian Structure Learning in Sparse Graphical Models

• Activity Number: 4
• Type: Invited
• Date/Time: Sunday, August 9, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Abdolreza Mohammadi* and Ernst C. Wit
• Companies: University of Groningen and University of Groningen
• Keywords: Bayesian structure learning ; Sparse Gaussian graphical models ; Birth-death Markov chain Monte Carlo ; Gaussian Copula ; Exponential random graph ; Network inference

Abstract

One of the main issues in science is to decode complex relationships among large numbers of variables with few observations. One way to describe these relationships is by means of a network. Frequentist inference cannot easily explore the landscape of competing networks. Up until now, Bayesian inference suffered from computational problems in dealing with large networks. In this talk, we provide an efficient Bayesian framework for modelling networks by means of graphical models, that outperforms alternative Bayesian approaches in terms of convergence and computing time. Our proposed method is a trans-dimensional MCMC approach based on a birth-death process. It is easy to implement and computationally feasible for high-dimensional graphs. We extend the method to non-Gaussian data by using copula Gaussian graphical models. We apply the method to a Dupuytren disease dataset to discover potential risk factors and which fingers are jointly affected. Furthermore, we show how in the presence of potential covariates, exponential random graph models can be an informative prior for the graph structure. We have implemented the method in the R package BDgraph which is freely available online.