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
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Associated Event:
Computational Uncertainty Quantification: Mathematical Foundations, Methodology & Data (Thematic Programme)
Organizer(s):
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)