Estimating rank-one matrices with mismatched prior and noise: universality and large deviations
Probability
2025-01-07 v1
Abstract
We prove a universality result that reduces the free energy of rank-one matrix estimation problems in the setting of mismatched prior and noise to the computation of the free energy for a modified Sherrington-Kirkpatrick spin glass. Our main result is an almost sure large deviation principle for the overlaps between the truth signal and the estimator for both the Bayes-optimal and mismatched settings. Through the large deviations principle, we recover the limit of the free energy in mismatched inference problems and the universality of the overlaps.
Keywords
Cite
@article{arxiv.2306.09283,
title = {Estimating rank-one matrices with mismatched prior and noise: universality and large deviations},
author = {Alice Guionnet and Justin Ko and Florent Krzakala and Lenka Zdeborová},
journal= {arXiv preprint arXiv:2306.09283},
year = {2025}
}
Comments
54 pages