Conditional Expectation Propagation

TL;DR

Conditional Expectation Propagation (CEP) improves upon standard EP by enabling efficient, analytical fixed point iterations through conditional moment matching, enhancing inference quality and computational efficiency across various models.

Contribution

We introduce CEP, a novel method that performs conditional moment matching to overcome intractability and inefficiency in traditional EP algorithms.

Findings

CEP achieves better inference accuracy than standard EP.

CEP is more computationally efficient than Laplace propagation.

Experiments demonstrate CEP's versatility across multiple models.

Abstract

Expectation propagation (EP) is a powerful approximate inference algorithm. However, a critical barrier in applying EP is that the moment matching in message updates can be intractable. Handcrafting approximations is usually tricky, and lacks generalizability. Importance sampling is very expensive. While Laplace propagation provides a good solution, it has to run numerical optimizations to find Laplace approximations in every update, which is still quite inefficient. To overcome these practical barriers, we propose conditional expectation propagation (CEP) that performs conditional moment matching given the variables outside each message, and then takes expectation w.r.t the approximate posterior of these variables. The conditional moments are often analytical and much easier to derive. In the most general case, we can use (fully) factorized messages to represent the conditional moments by quadrature formulas. We then compute the expectation of the conditional moments via Taylor approximations when necessary. In this way, our algorithm can always conduct efficient, analytical fixed point iterations. Experiments on several popular models for which standard EP is available or unavailable demonstrate the advantages of CEP in both inference quality and computational efficiency.