Estimating rank-one matrices with mismatched prior and noise: universality and large deviations - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

Estimating rank-one matrices with mismatched prior and noise: universality and large deviations

Justin Ko
  • Fonction : Auteur
Florent Krzakala
  • Fonction : Auteur
Lenka Zdeborová
  • Fonction : Auteur

Résumé

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.

Dates et versions

hal-04230791 , version 1 (06-10-2023)

Identifiants

Citer

Alice Guionnet, Justin Ko, Florent Krzakala, Lenka Zdeborová. Estimating rank-one matrices with mismatched prior and noise: universality and large deviations. 2023. ⟨hal-04230791⟩
7 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More