Spike-And-Slab Group Lassos for Grouped Regression and Sparse Generalized Additive Models

• Activity Number: 572 - Sparsity and Variable Selection in Posterior Inference
• Type: Contributed
• Date/Time: Wednesday, July 31, 2019 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Ray Bai* and Gemma Moran and Joseph Antonelli
• Companies: and University of Pennsylvania and University of Florida
• Keywords: generalized additive model; regression with grouped variables; sparsity; spike-and-slab LASSO; posterior contraction; nonparametric regression

Abstract

We introduce the spike-and-slab group lasso (SSGL) for Bayesian estimation and variable selection in linear regression with grouped variables. We further extend the SSGL to sparse generalized additive models (GAMs), thereby introducing the first nonparametric variant of the spike-and-slab lasso methodology. Our model simultaneously performs group selection and estimation, while our fully Bayes treatment of the mixture prior allows for model complexity control and automatic self-adaptivity to different levels of sparsity. We develop theory to uniquely characterize the global posterior mode under the SSGL and introduce a highly efficient coordinate ascent algorithm for maximum a posteriori (MAP) estimation. We illustrate our methodology through simulations and data analysis.