[Statlist] ETH Young Data Science Researcher Seminar Zurich, Virtual Seminar by Sven Wang, University of Cambridge, 10 July 2020

[Maurer Letizia]

Dear all

We are glad to announce the following talk in the virtual ETH Young Data Science Researcher Seminar Zurich

"On polynomial-​time computation of high-​dimensional posterior measures by Langevin-​type algorithms"  
by Sven Wang, University of Cambridge

Time: Friday, 10 July 2020, 15:00-​16:00
Place: Zoom at https://ethz.zoom.us/j/92367940258

Abstract:The problem of generating random samples of high-​dimensional posterior distributions arising from Gaussian process priors is considered. The main results consist of non-​asymptotic computational guarantees for Langevin-​type MCMC algorithms which scale polynomially in key quantities such as the dimension of the model, the desired precision level, and the number of available statistical measurements. As a direct consequence, it is shown that posterior mean vectors as well as maximum a posteriori (MAP) estimates are computable in polynomial time, with high probability under the distribution of the data. These results are derived in a general high-​dimensional non-​linear regression setting where posterior measures are not necessarily log-​concave, employing a set of local `geometric' assumptions on the parameter space. The theory is illustrated in a representative example from PDEs involving a non-​linear inverse problem for the steady-​state Schrödinger equation.

M. Löffler, A. Taeb, Y. Chen

Seminar website: https://math.ethz.ch/sfs/news-and-events/young-data-science.html