A0936
Title: The multivariate spike-and-slab LASSO: Algorithms, asymptotics, and inference
Authors: Sameer Deshpande - University of Wisconsin--Madison (United States) [presenting]
Abstract: Multivariate linear regression models are considered to predict $q$ correlated responses (of possibly mixed type) using a common set of p predictors. The interest lies not only in determining whether a particular predictor has a direct or marginal effect on each response but also in understanding the residual dependence between the outcomes. A Bayesian procedure is proposed for such determination using continuous spike-and-slab priors. Rather than relying on a stochastic search through the high-dimensional parameter space, an Expectation Conditional Maximization algorithm targeting modal estimates of the matrix of regression coefficients and the residual precision matrix is developed. A key feature of the method is the model of the uncertainty about which parameters are negligible. Posterior contraction rates are further derived, and several strategies for quantifying posterior uncertainty are discussed.
