Posterior contraction in sparse generalized linear models

Model selection and minimax estimation in generalized linear models

Seonghyun Jeong and Subhashis Ghosal

Biometrika, 2021, vol. 108, issue 2, 367-379

Abstract: SummaryWe 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.

Keywords: Fractional posterior; Generalized linear model; High-dimensional regression; Posterior contraction rate; Sparsity-inducing prior (search for similar items in EconPapers)
Date: 2021
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