  We study Bayesian group-regularized estimation in high-dimensional
generalized linear models (GLMs) under a continuous spike-and-slab prior. Our
framework covers both canonical and non-canonical link functions and subsumes
logistic regression, Poisson regression, Gaussian regression, and negative
binomial regression with group sparsity. Under milder assumptions than those
previously assumed for the group lasso, we obtain the convergence rate for both
the maximum a posteriori (MAP) estimator and the full posterior distribution.
Our theoretical results thus justify the use of the posterior mode as a point
estimator. Furthermore, the posterior distribution contracts at the same rate
as the MAP estimator, an attractive feature of our approach which is not the
case for the group lasso. For computation, we propose an
expectation-maximization (EM) algorithm for rapidly obtaining MAP estimates
under our model. We illustrate our method through simulations and a real data
application on predicting human immunodeficiency virus (HIV) drug resistance
from protein sequences.
