Refreshments: 10:30 AM

Seminar: 11:00 AM

Title: A statistical perspective on algorithm unrolling models for inverse problems

Abstract: We consider inverse problems where the forward model, that is the conditional distribution of the observation y  given the latent variable of interest x  is known, and access is given to a data set in which multiple instances of (x,y) are 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 properties of the gradient descent network (GDN), a well-known architecture driven by proximal gradient descent that epitomizes unrolling learning. Under some regularity conditions, we show that when d_y ≥d_x, the GDN estimator solves the inverse problem at a statistical rate faster than the nonparametric minimax rate achievable while ignoring the forward model. Furthermore, our results are explicit in the unrolling depth of the network and suggest that unrolling models are typically prone to overfitting as the unrolling depth
increases, and careful tuning as function of the sample size is required for best performances. We provide several examples to illustrate these results.