期刊
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
卷 113, 期 521, 页码 431-444出版社
AMER STATISTICAL ASSOC
DOI: 10.1080/01621459.2016.1260469
关键词
High-dimensional regression; LASSO; Penalized likelihood; Posterior concentration; Spike-and-Slab; Variable selection
资金
- James S. Kemper Foundation Faculty Research Fund at the University of Chicago Booth School of Business
- NSF [DMS -1406563]
- Direct For Mathematical & Physical Scien [1406563] Funding Source: National Science Foundation
Despite the wide adoption of spike-and-slab methodology for Bayesian variable selection, its potential for penalized likelihood estimation has largely been overlooked. In this article, we bridge this gap by cross-fertilizing these two paradigms with the Spike-and-Slab LASSO procedure for variable selection and parameter estimation in linear regression. We introduce a new class of self-adaptive penalty functions that arise from a fully Bayes spike-and-slab formulation, ultimately moving beyond the separable penalty framework. A virtue of these nonseparable penalties is their ability to borrow strength across coordinates, adapt to ensemble sparsity information and exert multiplicity adjustment. The Spike-and-Slab LASSO procedure harvests efficient coordinate-wise implementations with a path-following scheme for dynamic posterior exploration. We show on simulated data that the fully Bayes penalty mimics oracle performance, providing a viable alternative to cross-validation. We develop theory for the separable and nonseparable variants of the penalty, showing rate-optimality of the global mode as well as optimal posterior concentration when p > n. Supplementary materials for this article are available online.
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