Department of Mathematics - Seminar on Statistics - Graphical regression with covariates in high Dimensions

While covariance matrices have been widely studied in many scientific fields, relatively limited progress has been made on estimating conditional covariances that permits a large covariance matrix to vary with high-dimensional subject-level covariates. In this talk, we present a new sparse covariance regression framework that models the covariance matrix as a function of subject-level covariates. In the context of co-expression quantitative trait locus (QTL) studies, our method can be used to determine if and how gene co-expressions vary with genetic variations. We approach parameter estimation with a coordinate descent algorithm and investigate the $\ell_1$ and $\ell_2$ convergence rate of the estimated parameters. In addition, we propose a computationally efficient debiased inference procedure for uncertainty quantification. The utility of the proposed method is demonstrated through an application to a gene co-expression network study with brain cancer patients.