Uncertainty quantification for learned ISTA
Frederik Hoppe Claudio Mayrink Verdun Felix Krahmer Hannah Laus Holger Rauhut
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.