[Statlist] Zurich Colloquium in Applied and Computational Mathematics, Virtual Seminar by Prof. Dr. Jakob Zech, Uni Heidelberg, Germany, 21 October 2020 16:15-​17:15

[Maurer Letizia]

Dear all

Zurich Colloquium in Applied and Computational Mathematics is glad to announce the following talk 

"Sparse approximation of triangular transports on bounded domains"  
by Prof. Dr. Jakob Zech, Uni Heidelberg, Germany

Time: Wednesday, 21 October 2020, 16:15-​17:15
Place: Zoom https://math.ethz.ch/sam/news-and-events/zhacm-colloquia.html 

Abstract: Transport maps coupling two different measures can be used to sample from arbitrarily complex distributions. One of the main applications of this approach concerns Bayesian inference, where sampling from a posterior distribution facilitates making predictions based on partial and noisy measurments. In this talk we investigate the approximation of triangular transports $T:[-1,1]^d\to [-1,1]^d$ on the $d$-​dimensional unit cube by polynomial expansions and ReLU networks. Specifically, given a reference and a target probability measure with positive and analytic Lebesgue densities on $[-1,1]^d$, we show that the unique Knothe-​Rosenblatt transport, which pushes forward the reference to the target, can be approximated at an exponential rate in case $d<\infty$. These results are generalized to $d=\infty$, within a setting which incorporates many posterior densities occurring in PDE-​driven Bayesian inverse problems. In the infinite dimensional case ($d=\infty$) we verify an algebraic convergence rate, which shows that the curse of dimensionality can be overcome.

Best wishes,



Seminar website: https://math.ethz.ch/sam/news-and-events/zhacm-colloquia.html