Sparse Estimation of Network: An Approximate Bayesian Approach

• Activity Number: 313
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Nilabja Guha*
• Companies: Texas A&M University
• Keywords: Graphical model ; Mean field approximation

Abstract

Graphical model can be used to describe the interdependence of the variables for various kind of data sets such as gene expression. In a graphical model the variables are denoted by nodes and an edge between two nodes is present if the two corresponding variables are dependent. For Gaussian graphical model (GGM), when a multivariate normal joint distribution is present between the variables, looking at the precision matrix is useful. An element of precision matrix is zero if the partial correlation between the variables is zero and the corresponding edge does not exist.

We propose a Bayesian, quantile based method for sparse estimation of network, estimating the posterior graph by mean field approximation. The resulting graph estimation is robust to outliers and applicable under general distributional assumptions. We investigate the performance under different distributional set up and on gene expression data and compare with the standard methodology where the proposed methodology performs better in detecting the underlying network.