Novel Sampling-Based Methods for High-Dimensional Inference

Datum

04.12.2019

Zeit

17:00 - 18:00

Sprecher

Prof. Dr. Robert Scheichl

Zugehörigkeit

Universität Heidelberg

Serie

TUD Dresdner Mathematisches Seminar

Sprache

de

Hauptthema

Mathematik

Host

Prof. Dr. Oliver Sander (Institut für Numerische Mathematik)

Beschreibung

High- or infinite-dimensional inverse problems in the context of complex physical systems arise in many science and engineering
applications. Sampling-based inference methods provide an approach that allows in principle to solve this problem and to provide a quantification of uncertainties without suffering from the curse of dimensionality. In contrast to the very popular deep neural network approaches in machine learning, they provide a theoretical framework that allows in most cases to rigorously analyse their performance and complexity. However, to bring these sampling methods in the feasible range for practical problems it is in general necessary to improve classical sampling approaches, such as random-walk Metropolis-Hastings MCMC.

Stein variational gradient descent (SVGD) was recently proposed as a general purpose nonparametric variational inference algorithm: it minimises the Kullback–Leibler divergence between the target distribution and its approximation by implementing a form of functional gradient descent on a reproducing kernel Hilbert space [Liu & Wang, NIPS 2016]. In the main part of the talk, I will present a way how to accelerate and generalise the SVGD algorithm by including second-order information, thereby approximating a Newton-like iteration in function space. We also show how second-order information can lead to more effective choices of kernel. We observe significant computational gains over the original SVGD algorithm in multiple test cases.

In the final part of the talk, I will present a few alternative approaches for accelerating sampling-based inference methods, such as low-rank tensor surrogates and multilevel ideas. The talk presents joint work with G. Detommaso and S. Dolgov (Bath), T. Cui (Monash), C. Fox (Otago), Y. Marzouk and A. Spantini (MIT).

Links

• https://tu-dresden.de/mn/math/die-fakultaet/veranstaltungen/dms

Letztmalig verändert: 02.10.2019, 12:33:15