Uncertainty quantification for learned ISTA

TL;DR

This paper introduces a method to quantify uncertainty in the LISTA estimator, enhancing the interpretability of model-based deep learning solutions for inverse problems.

Contribution

It provides a rigorous approach to obtain confidence intervals for LISTA, addressing the lack of uncertainty quantification in algorithm unrolling schemes.

Findings

Proposes a method for confidence interval estimation in LISTA.

Bridges the gap between deep learning and statistical uncertainty quantification.

Enhances interpretability of model-based deep learning solutions.

Abstract

Model-based deep learning solutions to inverse problems have attracted increasing attention in recent years as they bridge state-of-the-art numerical performance with interpretability. In addition, the incorporated prior domain knowledge can make the training more efficient as the smaller number of parameters allows the training step to be executed with smaller datasets. Algorithm unrolling schemes stand out among these model-based learning techniques. Despite their rapid advancement and their close connection to traditional high-dimensional statistical methods, they lack certainty estimates and a theory for uncertainty quantification is still elusive. This work provides a step towards closing this gap proposing a rigorous way to obtain confidence intervals for the LISTA estimator.