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

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.

arXiv comment54 pages

References in corpus (20)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• Statistical physics of inference: Thresholds and algorithms
• Phase diagram of glassy systems in an external field
• General properties of overlap probability distributions in disordered spin systems. Toward Parisi ultrametricity
• Mutual information for symmetric rank-one matrix estimation: A proof of the replica formula
• Phase Transitions in Semidefinite Relaxations
• MMSE of probabilistic low-rank matrix estimation: Universality with respect to the output channel
• Information-theoretic thresholds from the cavity method
• Constrained Low-rank Matrix Estimation: Phase Transitions, Approximate Message Passing and Applications
• Mutual Information in Rank-One Matrix Estimation
• Spectral gap estimates in mean field spin glasses
• Estimation in the spiked Wigner model: A short proof of the replica formula
• Some Properties of the Phase Diagram for Mixed $p$-Spin Glasses
• The solution of the deep Boltzmann machine on the Nishimori line
• An inference problem in a mismatched setting: a spin-glass model with Mattis interaction
• Chaos in temperature in generic 2p-spin models
• The multi-species mean-field spin-glass on the Nishimori line
• Large deviations of glassy effective potentials
• Statistical mechanics of the maximum-average submatrix problem
• The ${\ell }^p$-Gaussian-Grothendieck problem with vector spins

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