Uncertainty Quantification for Learned ISTA

MCML Authors

Claudio Mayrink Verdun

Dr.

* Former Member

→ Group Felix Krahmer
 Optimization & Data Analysis

Hannah Laus

→ Group Felix Krahmer
 Optimization & Data Analysis

Felix Krahmer

Prof. Dr.

Principal Investigator

Optimization & Data Analysis

Holger Rauhut

Prof. Dr.

Principal Investigator

Mathematical Data Science and Artificial Intelligence

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.

inproceedings

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MLSP 2023

IEEE Workshop on Machine Learning for Signal Processing. Rome, Italy, Sep 17-20, 2023.

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Authors

F. Hoppe • C. M. Verdun • H. Laus • F. Krahmer • H. Rauhut

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Links

DOI

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Research Area

 A2 | Mathematical Foundations