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Statistical Physics of Linear and Bilinear Inference Problems by Schülke, Christophe is a scholarly article available to read on EtoBox.

What is Statistical Physics of Linear and Bilinear Inference Problems about?

The recent development of compressed sensing has led to spectacular advances in the understanding of sparse linear estimation problems as well as in algorithms to solve them. It has also triggered a new wave of developments in the related fields of generalized linear and bilinear inference problems, that have very diverse applications in signal processing and are furthermore a building block of deep neural networks. These problems have in common that they combine a linear mixing step and a nonlinear, probabilistic sensing step, producing indirect measurements of a signal of interest. Such a setting arises in problems as different as medical or astronomical imaging, clustering, matrix completion or blind source separation. The aim of this thesis is to propose efficient algorithms for this class of problems and to perform their theoretical analysis. To this end, it uses belief propagation, thanks to which high-dimensional distributions can be sampled efficiently, thus making a Bayesian approach to inference tractable. The resulting algorithms undergo phase transitions just as physical systems do. These phase transitions can be analyzed using the replica method, initially developed in

Author

Schülke, Christophe

Published

2016

Language

EN