# Expectation Propagation for Approximate Inference: Free Probability Framework

arXiv: https://arxiv.org/abs/1801.05411 · HTML: https://mlsanity.com/paper/1801.05411/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2018.

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

- [Memory Approximate Message Passing](https://mlsanity.com/paper/2106.02237/) (2021)
- [Analysis of Random Sequential Message Passing Algorithms for Approximate Inference](https://mlsanity.com/paper/2202.08198/) (2022)
- [Capacity Optimality of OAMP in Coded Large Unitarily Invariant Systems](https://mlsanity.com/paper/2206.11680/) (2022)

## Abstract (arXiv)

We study asymptotic properties of expectation propagation (EP) -- a method for approximate inference originally developed in the field of machine learning. Applied to generalized linear models, EP iteratively computes a multivariate Gaussian approximation to the exact posterior distribution. The computational complexity of the repeated update of covariance matrices severely limits the application of EP to large problem sizes. In this study, we present a rigorous analysis by means of free probability theory that allows us to overcome this computational bottleneck if specific data matrices in the problem fulfill certain properties of asymptotic freeness. We demonstrate the relevance of our approach on the gene selection problem of a microarray dataset.