Statistical inverse problems and gradient flow structures in the space of probability measures
Speaker: Prof. Dr. Sebastian Reich
Affiliation: Univesität Potsdam, Germany
Zoom link: Meeting ID: 923 1605 7419 , Passcode: 000474
Abstract: Statistical inverse problems lead to complex optimisation and/or Monte Carlo
sampling problems. Gradient descent and Langevin samplers are typically examples of
widely used algorithms. In my talk, I will present recent results on optimisation and sampling
algorithms, which can be viewed as interacting particle systems, and their mean-field limits.
I will highlight the geometric structure of these mean-field equations within the, so called, Otto
calculus, that is, a gradient flow structure in the space of probability measures. An important outcome
of recent work on the subject are affine invariant formulations, a property shared with Newton’s
method, but not with gradient descent and ordinary Langevin samplers.