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Paper IDL.7.2
Paper Title High-dimensional rank-one nonsymmetric matrix decomposition: the spherical case
Authors Clément Luneau, Nicolas Macris, EPFL, Switzerland; Jean Barbier, ICTP, Italy
Session L.7: High-dimensional Statistics
Presentation Lecture
Track Statistics and Learning Theory
Manuscript  Click here to download the manuscript
Virtual Presentation  Click here to watch in the Virtual Symposium
Abstract We consider the problem of estimating a rank-one nonsymmetric matrix under additive white Gaussian noise. The matrix to estimate can be written as the outer product of two vectors and we look at the special case in which both vectors are uniformly distributed on spheres. We prove a replica-symmetric formula for the average mutual information between these vectors and the observations in the high-dimensional regime. This goes beyond previous results which considered vectors with independent and identically distributed elements. The method used can be extended to rank-one tensor problems.

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2021 IEEE International Symposium on Information Theory

11-16 July 2021 | Melbourne, Victoria, Australia

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