  We present a Bayesian method for feature selection in the presence of
grouping information with sparsity on the between- and within group level.
Instead of using a stochastic algorithm for parameter inference, we employ
expectation propagation, which is a deterministic and fast algorithm. Available
methods for feature selection in the presence of grouping information have a
number of short-comings: on one hand, lasso methods, while being fast,
underestimate the regression coefficients and do not make good use of the
grouping information, and on the other hand, Bayesian approaches, while
accurate in parameter estimation, often rely on the stochastic and slow Gibbs
sampling procedure to recover the parameters, rendering them infeasible e.g.
for gene network reconstruction. Our approach of a Bayesian sparse-group
framework with expectation propagation enables us to not only recover accurate
parameter estimates in signal recovery problems, but also makes it possible to
apply this Bayesian framework to large-scale network reconstruction problems.
The presented method is generic but in terms of application we focus on gene
regulatory networks. We show on simulated and experimental data that the method
constitutes a good choice for network reconstruction regarding the number of
correctly selected features, prediction on new data and reasonable computing
time.
