A multi-scale cavity method, with application to sub-linear rank matrix denoising (Jean Barbier, ICTP)

11.03.2024 16:15 – 18:15

The cavity method is a powerful approach from the mathematical physics of spin glasses allowing to rigorously tackle the computation of log-partition functions and order parameters in mean-field spin models. I will present a generalization which allows to treat models where the variables are not simple finite-dimensional spins but are instead matrices whose dimensions M,N both grow in the thermodynamic limit; this in contrast with standard spin models where only one parameter, the number N of variables in the system, grows large. I will present the method in the context of an inference problem known as matrix denoising, in the challenging regime where the matrix to infer has a rank M (slowly) growing with its size N.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-15, Séminaire "Maths-Physique"

entrée libre