# Probability and Mathematical Physics Seminar

#### Phase transitions in generalized linear models

Speaker: Léo Miolane, NYU Courant and Center for Data Science

Location: Warren Weaver Hall 1302

Date: Friday, December 6, 2019, 11:10 a.m.

Synopsis:

This is a joint work with Jean Barbier, Florent Krzakala, Nicolas Macris and Lenka Zdeborova.

We consider generalized linear models (GLMs) where an unknown $n$-dimensional signal vector is observed through the application of a random matrix and a (non-linear)  componentwise output function.

We study the models in the high-dimensional limit, where the observation consists of $m$ points, and $m/n \to \alpha > 0$ as $n \to \infty$. This situation is ubiquitous in applications ranging from supervised machine learning to signal processing.

We will observe some phase transition phenomena. Depending on the noise level, the distribution of the signal and the non-linear function of the GLM we may encounter various scenarios where it may be possible or not to recover the signal.