Upcoming Event: Oden Institute Distinguished Lecture in Computational and Data Sciences

Generative Modelling using Schrödinger Bridges and Data-driven Modelling of Stochastic Processes

Sebastian Reich, Professor, University of Potsdam

Abstract

I will consider the generative problem of sampling from an unknown distribution for which only a sufficiently large number of training samples are available. The general approach is that of plug & play Langevin dynamics where the required data-driven drift term is approximated using Schrödinger bridges. A key bottleneck of this approach is the exponential dependence of the required training samples on the dimension, d, of the ambient state space. I will discuss a localization strategy which exploits conditional independence of conditional expectation values. Localization thus replaces a single high-dimensional Schrödinger bridge problem by d  low-dimensional Schrödinger bridge problems over the available training samples. In this context, a connection to multi-head self attention transformer architectures is established. As for the original Schrödinger bridge sampling approach, the localized sampler is stable and geometric ergodic. The sampler also naturally extends to conditional sampling and to Bayesian inference. I will demonstrate the performance of the proposed scheme through experiments on a Gaussian problem with increasing dimensions and several problems involving inferring stochastic processes from given time-series.

 

Biography

PhD in Electrical Engineering from the Technical University of Dresden in 1991. Habilitation in Mathematics from Freie Universität Berlin in 1998. Lecturer at University of Surrey, Reader and Professor at Imperial College London, Professor at University of Potsdam since 2004. SIAM Dahlquist Prize in 2003. SIAM Fellow Class 2019. Speaker Collaborative Research Centre, SFB 1294, on Data Assimilation since 2017. EIC of SIAM/ASA Journal on Uncertainty Quantification since 2021.