Emergent Mind

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

(1802.08963)
Published Feb 25, 2018 in cs.IT , math-ph , math.IT , and math.MP

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.

We're not able to analyze this paper right now due to high demand.

Please check back later (sorry!).

Generate a summary of this paper on our Pro plan:

We ran into a problem analyzing this paper.

Newsletter

Get summaries of trending comp sci papers delivered straight to your inbox:

Unsubscribe anytime.