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

• 成果类型: Article
• 署名作者: Bai, Ray; Moran, Gemma E.; Antonelli, Joseph L.; Chen, Yong; Boland, Mary R.
• 署名单位: University of South Carolina System; University of South Carolina Columbia; Columbia University; State University System of Florida; University of Florida; University of Pennsylvania
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2020.1765784
• 发表日期: 2022
• 页码: 184-197
• 关键词: bayesian variable selection; linear-models; multivariate responses; prediction; adjustment

摘要

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 proportion 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 block coordinate ascent algorithm for maximum a posteriori estimation. We further employ de-biasing methods to provide uncertainty quantification of our estimates. Thus, implementation of our model avoids the computational intensiveness of Markov chain Monte Carlo in high dimensions. We derive posterior concentration rates for both grouped linear regression and sparse GAMs when the number of covariates grows at nearly exponential rate with sample size. Finally, we illustrate our methodology through extensive simulations and data analysis.for this article are available online.