# Bounding errors of Expectation-Propagation

arXiv: https://arxiv.org/abs/1601.02387 · HTML: https://mlsanity.com/paper/1601.02387/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jan 2016.

## Built on by (most cited first, 3 of 3)

- [Federated Learning as Variational Inference: A Scalable Expectation Propagation Approach](https://mlsanity.com/paper/2302.04228/) (2023)
- [Streaming Factor Trajectory Learning for Temporal Tensor Decomposition](https://mlsanity.com/paper/2310.17021/) (2023)
- [Low-rank variational Bayes correction to the Laplace method](https://mlsanity.com/paper/2111.12945/) (2021)

## Abstract (arXiv)

Expectation Propagation is a very popular algorithm for variational inference, but comes with few theoretical guarantees. In this article, we prove that the approximation errors made by EP can be bounded. Our bounds have an asymptotic interpretation in the number n of datapoints, which allows us to study EP's convergence with respect to the true posterior. In particular, we show that EP converges at a rate of 0(n-2) for the mean, up to an order of magnitude faster than the traditional Gaussian approximation at the mode. We also give similar asymptotic expansions for moments of order 2 to 4, as well as excess Kullback-Leibler cost (defined as the additional KL cost incurred by using EP rather than the ideal Gaussian approximation). All these expansions highlight the superior convergence properties of EP. Our approach for deriving those results is likely applicable to many similar approximate inference methods. In addition, we introduce bounds on the moments of log-concave distributions that may be of independent interest.