Fundamental limits of low-rank matrix estimation: the non-symmetric case

Léo Miolane 1
1 DYOGENE - Dynamics of Geometric Networks
DI-ENS - Département d'informatique de l'École normale supérieure, CNRS - Centre National de la Recherche Scientifique : UMR 8548, Inria de Paris
Abstract : We consider the high-dimensional inference problem where the signal is a low-rank matrix which is corrupted by an additive Gaussian noise. Given a probabilistic model for the low-rank matrix, we compute the limit in the large dimension setting for the mutual information between the signal and the observations, as well as the matrix minimum mean square error, while the rank of the signal remains constant. This allows to locate the information-theoretic threshold for this estimation problem, i.e. the critical value of the signal intensity below which it is impossible to recover the low-rank matrix.
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https://hal.archives-ouvertes.fr/hal-01648369
Contributor : Léo Miolane <>
Submitted on : Saturday, November 25, 2017 - 4:22:12 PM
Last modification on : Wednesday, January 30, 2019 - 11:07:56 AM

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  • HAL Id : hal-01648369, version 1
  • ARXIV : 1702.00473

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Léo Miolane. Fundamental limits of low-rank matrix estimation: the non-symmetric case. 2017. ⟨hal-01648369⟩

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