  Exact inference in the linear regression model with spike and slab priors is
often intractable. Expectation propagation (EP) can be used for approximate
inference. However, the regular sequential form of EP (R-EP) may fail to
converge in this model when the size of the training set is very small. As an
alternative, we propose a provably convergent EP algorithm (PC-EP). PC-EP is
proved to minimize an energy function which, under some constraints, is bounded
from below and whose stationary points coincide with the solution of R-EP.
Experiments with synthetic data indicate that when R-EP does not converge, the
approximation generated by PC-EP is often better. By contrast, when R-EP
converges, both methods perform similarly.
