  Expectation propagation (EP) is a family of algorithms for performing
approximate inference in probabilistic models. The updates of EP involve the
evaluation of moments -- expectations of certain functions -- which can be
estimated from Monte Carlo (MC) samples. However, the updates are not robust to
MC noise when performed naively, and various prior works have attempted to
address this issue in different ways. In this work, we provide a novel
perspective on the moment-matching updates of EP; namely, that they perform
natural-gradient-based optimisation of a variational objective. We use this
insight to motivate two new EP variants, with updates that are particularly
well-suited to MC estimation; they remain stable and are most sample-efficient
when estimated with just a single sample. These new variants combine the
benefits of their predecessors and address key weaknesses. In particular, they
are easier to tune, offer an improved speed-accuracy trade-off, and do not rely
on the use of debiasing estimators. We demonstrate their efficacy on a variety
of probabilistic inference tasks.
