# Sparse Estimation with the Swept Approximated Message-Passing Algorithm

arXiv: https://arxiv.org/abs/1406.4311 · HTML: https://mlsanity.com/paper/1406.4311/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jun 2014.

## Built on by (most cited first, 2 of 2)

- [Memory Approximate Message Passing](https://mlsanity.com/paper/2106.02237/) (2021)
- [An adaptive shortest-solution guided decimation approach to sparse high-dimensional linear regression](https://mlsanity.com/paper/2211.15057/) (2022)

## Abstract (arXiv)

Approximate Message Passing (AMP) has been shown to be a superior method for inference problems, such as the recovery of signals from sets of noisy, lower-dimensionality measurements, both in terms of reconstruction accuracy and in computational efficiency. However, AMP suffers from serious convergence issues in contexts that do not exactly match its assumptions. We propose a new approach to stabilizing AMP in these contexts by applying AMP updates to individual coefficients rather than in parallel. Our results show that this change to the AMP iteration can provide theoretically expected, but hitherto unobtainable, performance for problems on which the standard AMP iteration diverges. Additionally, we find that the computational costs of this swept coefficient update scheme is not unduly burdensome, allowing it to be applied efficiently to signals of large dimensionality.