Publication

The Mutual Information in Random Linear Estimation Beyond i.i.d. Matrices

Nicolas Macris, Jean François Emmanuel Barbier, Florent Gérard Krzakala
2018
Conference Papers

Abstract

There has been definite progress recently in proving the variational single-letter formula given by the heuristic replica method for various estimation problems. In particular, the replica formula for the mutual information in the case of noisy linear estimation with random i.i.d. matrices, a problem with applications ranging from compressed sensing to statistics, has been proven rigorously. In this contribution we go beyond the restrictive i.i.d. matrix assumption and discuss the formula proposed by Takeda, Uda, Kabashima and later by Tulino, Verdu, Caire and Shamai who used the replica method. Using the recently introduced adaptive interpolation method and random matrix theory, we prove this formula for a relevant large sub-class of rotationally invariant matrices.

Official source

https://infoscience.epfl.ch/entities/publication/03826a2d-516d-4b93-a8ca-fdd9ebc42667

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Nicolas Macris, Jean François Emmanuel Barbier, Florent Gérard Krzakala
2018
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/03826a2d-516d-4b93-a8ca-fdd9ebc42667

About this result

Related concepts (30)

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In probability theory and statistics, a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the covariance between each pair of elements of a given random vector. Any covariance matrix is symmetric and positive semi-definite and its main diagonal contains variances (i.e., the covariance of each element with itself). Intuitively, the covariance matrix generalizes the notion of variance to multiple dimensions.

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