Uncertainty quantification for learned ISTA

• URL: http://arxiv.org/abs/2309.07982v1
• Date: Thu, 14 Sep 2023 18:39:07 GMT
• Title: Uncertainty quantification for learned ISTA
• Authors: Frederik Hoppe, Claudio Mayrink Verdun, Felix Krahmer, Hannah Laus, Holger Rauhut
• Abstract summary: Algorithm unrolling schemes stand out among these model-based learning techniques. They lack certainty estimates and a theory for uncertainty quantification is still elusive. This work proposes a rigorous way to obtain confidence intervals for the LISTA estimator.
• Score: 5.706217259840463
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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