# Expectation Consistent Approximate Inference: Generalizations and Convergence

arXiv: https://arxiv.org/abs/1602.07795 · HTML: https://mlsanity.com/paper/1602.07795/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2016.

## Built on by (most cited first, 6 of 6)

- [Phase Retrieval using Expectation Consistent Signal Recovery Algorithm based on Hypernetwork](https://mlsanity.com/paper/2101.04348/) (2021)
- [Fundamental Limits of Two-layer Autoencoders, and Achieving Them with Gradient Methods](https://mlsanity.com/paper/2212.13468/) (2022)
- [Denoising Generalized Expectation-Consistent Approximation for MR Image Recovery](https://mlsanity.com/paper/2206.05049/) (2022)
- [Fast and Robust Phase Retrieval via Deep Expectation-Consistent Approximation](https://mlsanity.com/paper/2407.09687/) (2024)
- [Towards Designing Optimal Sensing Matrices for Generalized Linear Inverse Problems](https://mlsanity.com/paper/2111.03237/) (2021)
- [Estimation of embedding vectors in high dimensions](https://mlsanity.com/paper/2312.07802/) (2023)

## Abstract (arXiv)

Approximations of loopy belief propagation, including expectation propagation and approximate message passing, have attracted considerable attention for probabilistic inference problems. This paper proposes and analyzes a generalization of Opper and Winther's expectation consistent (EC) approximate inference method. The proposed method, called Generalized Expectation Consistency (GEC), can be applied to both maximum a posteriori (MAP) and minimum mean squared error (MMSE) estimation. Here we characterize its fixed points, convergence, and performance relative to the replica prediction of optimality.