Sparse Covariance Estimation in Heterogeneous Samples

• Activity Number: 373
• Type: Invited
• Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Abel Rodriguez*+ and Adrian Dobra and Alex Lenkoski
• Companies: University of California at Santa Cruz and University of Washington and University Heidelberg
• Keywords: Gaussian Graphical Model ; Mixture Model ; Dirichlet Process

Abstract

Standard Gaussian graphical models implicitly assume that the conditional independence among variables is common to all observations in the sample. However, in practice, observations are usually collected from heterogeneous populations where such an assumption is not satisfied, leading in turn to nonlinear relationships among variables. To address such situations we explore mixtures of Gaussian graphical models; in particular, we consider both infinite mixtures and infinite hidden Markov models where the emission distributions correspond to Gaussian graphical models. Such models allow us to divide a heterogeneous population into homogenous groups, with each cluster having its own conditional independence structure. As an illustration, we study the trends in foreign exchange rate fluctuations in the pre-Euro era.