The adaptive interpolation method for proving replica formulas. Applications to the Curie-Weiss and Wigner spike models
Disordered Systems and Neural Networks
2020-03-10 v2 Information Theory
Mathematical Physics
math.IT
math.MP
Probability
Abstract
In this contribution we give a pedagogic introduction to the newly introduced adaptive interpolation method to prove in a simple and unified way replica formulas for Bayesian optimal inference problems. Many aspects of this method can already be explained at the level of the simple Curie-Weiss spin system. This provides a new method of solution for this model which does not appear to be known. We then generalize this analysis to a paradigmatic inference problem, namely rank-one matrix estimation, also refered to as the Wigner spike model in statistics. We give many pointers to the recent literature where the method has been succesfully applied.
Keywords
Cite
@article{arxiv.1901.06516,
title = {The adaptive interpolation method for proving replica formulas. Applications to the Curie-Weiss and Wigner spike models},
author = {Jean Barbier and Nicolas Macris},
journal= {arXiv preprint arXiv:1901.06516},
year = {2020}
}