Simultaneous variable and covariance selection with the multivariate spike-and-slab LASSO

Abstract : We propose a Bayesian procedure for simultaneous variable and covariance selection using continuous spike-and-slab priors in multivariate linear regression models where q possibly correlated responses are regressed onto p predictors. Rather than relying on a stochastic search through the high-dimensional model space, we develop an ECM algorithm similar to the EMVS procedure of Rockova and George targeting modal estimates of the matrix of regression coefficients and residual precision matrix. Varying the scale of the continuous spike densities facilitates dynamic posterior exploration and allows us to filter out negligible regression coefficients and partial covariances gradually. Our method is seen to substantially outperform regularization competitors on simulated data. We demonstrate our method with a re-examination of data from a recent observational study of the effect of playing high school football on several later-life cognition, psychological, and socio-economic outcomes.

The journal version of the paper is available at DOI:10.1080/10618600.2019.1593179.

A pre-print version of the paper is available at arXiv:1708.08911.

An R package implementing mSSL is available at this GitHub repo.

Download the journal version of the paper here.

A pre-print is available here.

Recommended citation: Deshpande, S.K., Rockova, V., and George, E.I. (2019). "Simultaneous variable and covariance selection with the multivariate spike-and-slab LASSO." Journal of Computational and Graphical Statistics. 28(4): 921--931.