title: Sparse covariance estimation in heterogeneous samples.
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.
authors.affiliation: Department of Applied Mathematics and Statistics, University of California, Santa Cruz, California.
authors.forename: Abel
authors.initials: A
authors.lastname: Rodríguez
authors.affiliation: Department of Applied Mathematics, Heidelberg University, Heidelberg, Germany.
authors.forename: Alex
authors.initials: A
authors.lastname: Lenkoski
authors.affiliation: Departments of Statistics, Biobehavioral Nursing and, Health Studies and the Center for Statistics and the Social Sciences, University of Washington, Seattle, Washington.
authors.forename: Adrian
authors.initials: A
authors.lastname: Dobra
keywords: Covariance selection; Dirichlet process; Gaussian graphical model; hidden Markov model; mixture model; nonparametric Bayes inference