Posterior contraction in sparse generalized linear models

• 成果类型: Article
• 署名作者: Jeong, Seonghyun; Ghosal, Subhashis
• 署名单位: Yonsei University; North Carolina State University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asaa074
• 发表日期: 2021
• 页码: 367379
• 关键词: CONVERGENCE-RATES; regression; FRAMEWORK

摘要

We study posterior contraction rates in sparse high-dimensional generalized linear models using priors incorporating sparsity. A mixture of a point mass at zero and a continuous distribution is used as the prior distribution on regression coefficients. In addition to the usual posterior, the fractional posterior, which is obtained by applying Bayes theorem with a fractional power of the likelihood, is also considered. The latter allows uniformity in posterior contraction over a larger subset of the parameter space. In our set-up, the link function of the generalized linear model need not be canonical. We show that Bayesian methods achieve convergence properties analogous to lasso-type procedures. Our results can be used to derive posterior contraction rates in many generalized linear models including logistic, Poisson regression and others.