Date: 2025-03-14

Time: 15:30-16:30 (Montreal time)

Location: In person, Burnside 1104

https://mcgill.zoom.us/j/88555780651

Meeting ID: 885 5578 0651

Passcode: None

Abstract:

We present a framework for solving linear inverse problems that is computationally tractable and has mathematical certificates. To this end, we interpret the ground truth of a linear inverse problem as a random vector with unknown distribution. We solve for a distribution which is close to a prior P (guessed or data-driven) measured in the KL-divergence while also having an expectation that yields high fidelity with the given data that defines the problem. After reformulation this yields a strictly convex, finite dimensional optimization problem whose regularizer, the MEM functional, is paired in duality with the log-moment generating function of the prior P. We exploit this computationally via Fenchel-Rockafellar duality. When no obvious guess for P is available, we use data to generate an empirical prior. Using techniques from variational analysis and stochastic optimization, we show that, and at what rate, the solution of the empirical problems converge (as the sample size grows) to the solution of the problem with known prior.

Speaker

Tim Hoheisel received his doctorate of mathematics from Julius-Maximilians University  (Würzburg) under the supervision of Christian Kanzow in 2009. He was a postdoctoral researcher there until 2016. During this time, he was a visiting professor at Heinrich-Heine University (Düsseldorf) in the winter semester 2011/12 as well as a visiting researcher at University of Washington (Seattle) under mentorship of James V. Burke in 2012 and 2014.  In 2016, he became an assistant professor at the department of mathematics and statistics at McGill University (Montreal) where he was awarded early tenure in 2021 and promoted to associate professor. Since 2022 he has been director of the applied mathematics laboratory at the “Centre de Recherches Mathématiques” in Montreal. His research interests lie in nonsmooth optimization and variational analysis where he is particularly interested in stability of nonsmooth problems arising in various applications.