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Jonathan Scarlett (National University of Singapore) – “Recent Developments in High-Dimensional Estimation with Generative Priors”

October 11 @ 3:00 pm - 4:15 pm
Statistical Seminar: Every Monday at 2:00 pm.
Time: 3:00 pm – 4:15 pm exceptionally
Date: 11th of October 2021
Place: visio

Jonathan Scarlett (National University of Singapore) – “Recent Developments in High-Dimensional Estimation with Generative Priors”

Abstract: The problem of estimating an unknown vector (or image) from linear or non-linear measurements has a long history in statistics, machine learning, and signal processing. Classical studies focus on the “n >> p” regime (#measurements >> #parameters), and more recent studies handle the “n << p” regime by exploiting low-dimensional structure such as sparsity or low-rankness. Such variants are commonly known as compressive sensing. In this talk, I will verview recent methods that move beyond these explicit notions of structure, and instead assume that the underlying vector is well-modeled by a data-riven generative model (e.g., produced by deep learning methods such as GANs). I will focus primarily on theoretical developments, including upper and lower bounds on the sample complexity in terms of various properties of the generative model, such as its number of latent (input) parameters, its Lipschitz constant, and its width and depth in the special case of neural network models. I will also discuss some developments regarding non-linear models, geometric roperties of the relevant optimization landscapes, and methods for fully general probabilistic priors.

Organizers:
Cristina BUTUCEA (CREST), Alexandre TSYBAKOV (CREST), Karim LOUNICI (CMAP) , Jaouad MOURTADA (CREST)
Sponsors:
CREST-CMAP