2015/02/28 by Joël Bun, Joel Bun, Romain Allez +2 · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Blind Source Separation Techniques #Eigenvalues and eigenvectors #Estimator #Invariant (physics) #Limit (mathematics) #Matrix (chemical analysis) #Multiplicative function #Multiplicative noise #Random Matrices and Applications #Rotational invariance #Symmetric matrix #cond-mat.stat-mech #math.PR #q-fin.MF
paper · pdf · doi:10.1109/tit.2016.2616132
19 pages, 9 figures
openalex created_date 2016/06/24 · openalex publication_date 2016/10/10 · arxiv created 2016/10/26 · arxiv updated 2016/10/28 · openalex updated_date 2026/08/05
We investigate the problem of estimating a given real symmetric signal matrix C from a noisy observation matrix M in the limit of large dimension. We consider the case where the noisy measurement M comes either from an arbitrary additive or multiplicative rotational invariant perturbation. We establish, using the replica method, the asymptotic global law estimate for three general classes of noisy matrices, significantly extending previously obtained results. We give exact results concerning the asymptotic deviations (called overlaps) of the perturbed eigenvectors away from the true ones, and we explain how to use these overlaps to “clean” the noisy eigenvalues of M. We provide some numerical checks for the different estimators proposed in this paper and we also make the connection with some well-known results of Bayesian statistics.