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Bayesian high-dimensional linear regression with generic ...
Bai Jiang, Qiang Sun · 2019-12-19 · via stat.ML updates on arXiv.org

Spike-and-slab priors are popular Bayesian solutions for high-dimensional linear regression problems. Previous theoretical studies on spike-and-slab methods focus on specific prior formulations and use prior-dependent conditions and analyses, and thus can not be generalized directly. In this paper, we propose a class of generic spike-and-slab priors and develop a unified framework to rigorously assess their theoretical properties. Technically, we provide general conditions under which generic spike-and-slab priors can achieve the nearly-optimal posterior contraction rate and the model selection consistency. Our results include those of Narisetty and He (2014) and Castillo et al. (2015) as special cases.