# Simultaneous Variable and Covariance Selection with the Multivariate Spike-and-Slab Lasso

arXiv: https://arxiv.org/abs/1708.08911 · HTML: https://mlsanity.com/paper/1708.08911/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Aug 2017.

## Built on by (most cited first, 3 of 3)

- [For high-dimensional hierarchical models, consider exchangeability of effects across covariates instead of across datasets](https://mlsanity.com/paper/2107.06428/) (2021)
- [Efficient Network Automatic Relevance Determination](https://mlsanity.com/paper/2506.12352/) (2025)
- [Multivariate regression modeling in integrative analysis via sparse regularization](https://mlsanity.com/paper/2304.07451/) (2023)

## Abstract (arXiv)

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 & George (2014) 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.