The weekly SILO Seminar Series is made possible through the generous support of the 3M Company and its Advanced Technology Group


with additional support from the Analytics Group of the Northwestern Mutual Life Insurance Company

Northwestern Mutual

Bayesian Covariance Regression and Autoregression

Emily Fox, Assistant Professor, University of Washington

Date and Time: Nov 28, 2012 (12:30 PM)
Location: Orchard room (3280) at the Wisconsin Institute for Discovery Building


Many inferential tasks, such as analyzing the functional connectivity of the brain via coactivation patterns or capturing the changing correlations amongst a set of assets for portfolio optimization, rely on modeling a covariance matrix whose elements evolve as a function of time. A number of multivariate heteroscedastic time series models have been proposed within the econometrics literature, but are typically limited by lack of clear margins, computational intractability, and curse of dimensionality. In this talk, we first introduce and explore a new class of time series models for covariance matrices based on a constructive definition exploiting inverse Wishart distribution theory. The construction yields a stationary, first-order autoregressive (AR) process on the cone of positive semi-definite matrices.

We then turn our focus to more general predictor spaces and scaling to high-dimensional datasets. Here, the predictor space could represent not only time, but also space or other factors. Our proposed Bayesian nonparametric covariance regression framework harnesses a latent factor model representation. In particular, the predictor-dependent factor loadings are characterized as a sparse combination of a collection of unknown dictionary functions (e.g, Gaussian process random functions). The induced predictor-dependent covariance is then a regularized quadratic function of these dictionary elements. Our proposed framework leads to a highly-flexible, but computationally tractable formulation with simple conjugate posterior updates that can readily handle missing data. Theoretical properties are discussed and the methods are illustrated through an application to the Google Flu Trends data and the task of word classification based on single-trial MEG data.

Emily Fox is an Assistant Professor in the Department of Statistics at the University of Washington, having joined in 2012 from a prior position at the Wharton Department of Statistics, University of Pennsylvania. From 2009-2011 she was a postdoc in the Duke Statistical Science Department, and received her S.B., M.Eng., E.E. and Ph.D. in EECS at MIT. Her doctoral thesis was awarded the 2009 Leonard J. Savage Thesis Award in Applied Methodology and the 2009 MIT EECS Jin-Au Kong Outstanding Doctoral Thesis Prize. Her research interests include Bayesian nonparametrics, Bayesian dynamic modeling and time series analysis. The work emphasizes methodology for high-dimensional, sparsely sampled data with applications in neuroscience, health monitoring, and finance, amongst others.