Uncertainty quantification for learned ISTA

arXiv (Cornell University)

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.

Authors 5

1. Frederik Hoppe Aachen Chair of Mathematics of Information Processing

   RWTH Aachen University

   Affiliation as printed

   Chair of Mathematics of Information Processing , RWTH Aachen University , Aachen , Germany

2. Claudio Mayrink Verdun

   Munich Center for Machine Learning · Technical University of Munich

   Affiliation as printed

   Department of Mathematics , Technical University of Munich , Munich , Germany

   Munich Center for Machine Learning , Munich , Germany

3. Felix Krahmer
4. Hannah Laus
5. Holger Rauhut Aachen Chair of Mathematics of Information Processing

   RWTH Aachen University

   Affiliation as printed

   Chair of Mathematics of Information Processing , RWTH Aachen University , Aachen , Germany