Student Probability Seminar

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On iterative Gaussian conditioning methods in high-dimensional statistics

Speaker: Cedric Gerbelot, NYU Courant

Location: Warren Weaver Hall WWH 202

Date: Wednesday, April 24, 2024, 12:30 p.m.

Synopsis:

A major challenge associated with the theory of modern, large-scale data analysis problems is their high-dimensional nature. Much of the classical statistical theory fails to hold in these setups where the ambient dimension is comparable or greater than the available number of samples, prompting the need for other theoretical tools. In this regard, the field of statistical physics of disordered systems and the related methods from high-dimensional probability propose a variety of interesting solutions. The goal of this talk will be to review one of these methods, the family of approximate message passing iterations, which enable to study the asymptotic properties of various high-dimensional systems using a low-dimensional recursion. We will then see how the associated proof technique can be used to study the dynamics of gradient-based descent algorithms with random data, giving a discrete form of the dynamical mean-field theory equations, an important tool in statistical physics.