[Statlist] FDS Seminar talk with Jakob Zech, Universität Heidelberg - 16 November 2023

[Maurer Letizia]

We are pleased to announce and invite you to the following talk in our FDS seminar series:

„Nonparametric Distribution Learning via Neural ODEs“
by Jakob Zech, Universität Heidelberg

Date and Time: Thursday, 16 November 2023, 16.15 - 17.15 (Zurich)
Place: ETH Zurich, HG G 19.1

Abstract: In this talk, we explore approximation properties and statistical aspects of Neural Ordinary Differential Equations (Neural ODEs). Neural ODEs are a recently established technique in computational statistics and machine learning, that can be used to characterize complex distributions. Specifically, given a fixed set of independent and identically distributed samples from a target distribution, the goal is either to estimate the target density or to generate new samples. We first investigate the regularity properties of the velocity fields used to push forward a reference distribution to the target. This analysis allows us to deduce approximation rates achievable through neural network representations. We then derive a concentration inequality for the maximum likelihood estimator of general ODE-​parametrized transport maps. By merging these findings, we are able to determine convergence rates in terms of both the network size and the number of required samples from the target distribution. Our discussion will particularly focus on target distributions within the class of positive $C^k$ densities on the $d$-​dimensional unit cube $[0,1]^d$.

Organisers: A. Bandeira, H. Bölcskei, P. Bühlmann, J. Peters, F. Yang


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