Seminar Series on the Mathematics of Data Science - Department of Applied Mathematics
With the MDS Seminar, we would like to launch a lecture series in which both researchers from the University of Twente and external researchers present their current work in the field of mathematics of data science. The aim is to get to know and understand the research of other groups and disciplines better. It offers the opportunity for regular exchange as well as a basis for possible collaborations.
Format
Seminars are held on campus and via Teams. All seminars occur every fortnight on Mondays at 4 p.m. unless otherwise stated (see the program below for the dates and the rooms).
Upcoming seminars
30 June 2025 (RA 2504)
- Speaker: prof.dr. Dirk Lorenz (University of Bremen)
Title: Bilevel learning of regularization of inverse problems—is it worth it?
Abstract:
We consider the problem of learning regularizers for linear discrete inverse problems. We focus on the supervised setting and on variational models. Our goal is to understand when and how this is possible. To that end, we do a theoretical analysis of affine linear regularization methods that are derived from quadratic Tikhonov regularization (we call the quadratic regularization and Lavrentiev regularization). This naturally leads to bilevel problems which we can turn into nonlinearly constrained optimization problems. We will identify situations in which Tikhonov does give good reconstruction quality in the least squares sense. On finding is: If one includes learning of the discrepancy term (i.e. we learn the noise covariance), all methods perform equal and best possible. We also show that if one does not learn the discrepancy term, Tikhonov regularization is worse than the other methods, depending on the interplay of the noise and the operator.
This is joint work with Sebastian Banert, Christoph Brauer and Lionel Tondji.