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arXiv · 2306.09283

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

Alice Guionnet·Justin Ko·Florent Krzakala·Lenka Zdeborová
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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.

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Alice Guionnet, Justin Ko, Florent Krzakala, Lenka Zdeborová. 2023-06-15. Estimating rank-one matrices with mismatched prior and noise: universality and large deviations. https://doi.org/10.1007/s00220-024-05179-0

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