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We study Bayesian group-regularized estimation in high-dimensionalgeneralized linear models (GLMs) under a continuous spike-and-slab prior. Ourframework covers both canonical and non-canonical link functions and subsumeslogistic regression, Poisson regression, Gaussian regression, and negativebinomial regression with group sparsity. Under milder assumptions than thosepreviously assumed for the group lasso, we obtain the convergence rate for boththe maximum a posteriori (MAP) estimator and the full posterior distribution.Our theoretical results thus justify the use of the posterior mode as a pointestimator. Furthermore, the posterior distribution contracts at the same rateas the MAP estimator, an attractive feature of our approach which is not thecase for the group lasso. For computation, we propose anexpectation-maximization (EM) algorithm for rapidly obtaining MAP estimatesunder our model. We illustrate our method through simulations and a real dataapplication on predicting human immunodeficiency virus (HIV) drug resistancefrom protein sequences.

Bayesian Group Regularization in Generalized Linear Models with a Continuous Spike-and-Slab Prior