Approximation and computation of triangular transport maps

Jakob Zech (U Heidelberg)

May 19. 2022, 11:00 — 11:45

One of the main challenges in Bayesian inference is to efficiently sample from high-dimensional "target" distributions such as the posterior, which is known only through its unnormalized density. A possible approach is to couple a tractible "reference" distribution with the target via a transport map, that approximately pushes forward the reference to the target. In this talk we discuss regularity and approximability of triangular transports for targets on bounded domains. Moreover, we present a multilevel optimization strategy to learn these maps by minimizing the KL-divergence. Here the term "level" may refer for instance to the accuracy of the numerical approximation of the forward map, and solving the corresponding optimization problem in a multilevel fashion can help to decrease computational costs. Finally, we outline how this multilevel strategy is applicable to optimization based inference algorithms more broadly.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Computational Uncertainty Quantification: Mathematical Foundations, Methodology & Data (Thematic Programme)
Clemens Heitzinger (TU Vienna)
Fabio Nobile (EPFL Lausanne)
Robert Scheichl (U Heidelberg)
Christoph Schwab (ETH Zürich)
Sara van de Geer (ETH Zürich)
Karen Willcox (U of Texas, Austin)