  We propose to learn a kernel-based message operator which takes as input all
expectation propagation (EP) incoming messages to a factor node and produces an
outgoing message. In ordinary EP, computing an outgoing message involves
estimating a multivariate integral which may not have an analytic expression.
Learning such an operator allows one to bypass the expensive computation of the
integral during inference by directly mapping all incoming messages into an
outgoing message. The operator can be learned from training data (examples of
input and output messages) which allows automated inference to be made on any
kind of factor that can be sampled.
