The Department of Statistics and Actuarial Science Spring Colloquium Series presents:

Qiuyun Zhu, PhD, Faculty Candidate for Assistant Professor in Statistics; Faragher Distinguished Postdoctoral Fellow, School of Statistics, University of Minnesota

“A Statistical Perspective on Algorithm Unrolling Models for Inverse Problems”

Abstract:

We consider inverse problems where the conditional distribution of the observation y given the latent variable of interest x (also known as the forward model) is known, and we have access to a data set in which multiple instances of x and y are both observed. In this context, algorithm unrolling has become a very popular approach for designing state-of-the-art deep neural network architectures that effectively exploit the forward model. We analyze the statistical complexity of the gradient descent network (GDN), an algorithm unrolling architecture driven by proximal gradient descent. We show the unrolling depth needed for the optimal statistical performance of GDNs. We also show that when the negative log-density of the latent variable x has a simple proximal operator, then a GDN unrolled at depth D′ can solve the inverse problem at some parametric rate. Our results thus also suggest that algorithm unrolling models are prone to overfitting as the unrolling depth D′ increases. We provide several examples to illustrate these results.

Meet and Greet at 3 p.m. in 241 SH. Colloquium at 3:30 p.m. in 71 SH.