Statistical inverse problems and gradient flow structures in the space of probability measures (S. Reich, Uni Potsdam, Germany)
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.