Matrix denoising via low-degree polynomials
Guilhem Semerjian
Lundi 03/06/2024, 11:00-12:00
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
In this talk I will discuss the additive version of the matrix denoising problem, where a random symmetric matrix S has to be inferred from the observation of Y=S+Z, with Z an independent random matrix modeling a noise. Systematic approximations to the Bayes-optimal estimator of S can be built by considering polynomial estimators. When the prior distributions on S and Z are orthogonally invariant this procedure allows to recover asymptotically the estimator introduced by Bun, Allez, Bouchaud and Potters in 2016. It also opens the way to the discussion of finite-size corrections, and to non-orthogonally invariant priors. A special case of particular interest occurs when S has a Wishart distribution, the denoising problem being then a simplified version of the extensive rank matrix factorization problem. Based on arXiv:2402.16719

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