  We introduce a class of generic spike-and-slab priors for high-dimensional
linear regression with grouped variables and present a Coordinate-ascent
Variational Inference (CAVI) algorithm for obtaining an optimal variational
Bayes approximation. Using parameter expansion for a specific, yet
comprehensive, family of slab distributions, we obtain a further gain in
computational efficiency. The method can be easily extended to fitting additive
models. Theoretically, we present general conditions on the generic
spike-and-slab priors that enable us to derive the contraction rates for both
the true posterior and the VB posterior for linear regression and additive
models, of which some previous theoretical results can be viewed as special
cases. Our simulation studies and real data application demonstrate that the
proposed method is superior to existing methods in both variable selection and
parameter estimation. Our algorithm is implemented in the R package GVSSB.
