AMP algorithms and Stein's method: Understanding TAP equations with a new method
Probability
2023-11-21 v1
Abstract
We propose a new iterative construction of solutions of the classical TAP equations for the Sherrington-Kirkpatrick model, i.e. with finite-size Onsager correction. The algorithm can be started in an arbitrary point, and converges up to the AT line. The analysis relies on a novel treatment of mean field algorithms through Stein's method. As such, the approach also yields weak convergence of the effective fields at all temperatures towards Gaussians, and can be applied, upon proper alterations, to all models where TAP-like equations and a Stein-operator are available.
Cite
@article{arxiv.2311.11924,
title = {AMP algorithms and Stein's method: Understanding TAP equations with a new method},
author = {Stephan Gufler and Adrien Schertzer and Marius A. Schmidt},
journal= {arXiv preprint arXiv:2311.11924},
year = {2023}
}
Comments
38 pages