  Several numerical approximation strategies for the expectation-propagation
algorithm are studied in the context of large-scale learning: the Laplace
method, a faster variant of it, Gaussian quadrature, and a deterministic
version of variational sampling (i.e., combining quadrature with variational
approximation). Experiments in training linear binary classifiers show that the
expectation-propagation algorithm converges best using variational sampling,
while it also converges well using Laplace-style methods with smooth factors
but tends to be unstable with non-differentiable ones. Gaussian quadrature
yields unstable behavior or convergence to a sub-optimal solution in most
experiments.
