Multi-fidelity No-U-Turn Sampling

Publikation: Beitrag in Buch/Bericht/KonferenzbandKonferenzbeitragBegutachtung

Abstract

Markov Chain Monte Carlo (MCMC) methods often take many iterations to converge for highly correlated or high-dimensional target density functions. Methods such as Hamiltonian Monte Carlo (HMC) or No-U-Turn Sampling (NUTS) use the first-order derivative of the density function to tackle the aforementioned issues. However, the calculation of the derivative represents a bottleneck for computationally expensive models. We propose to first build a multi-fidelity Gaussian Process (GP) surrogate. The building block of the multi-fidelity surrogate is a hierarchy of models of decreasing approximation error and increasing computational cost. Then the generated multi-fidelity surrogate is used to approximate the derivative. The majority of the computation is assigned to the cheap models thereby reducing the overall computational cost. The derivative of the multi-fidelity method is used to explore the target density function and generate proposals. We select or reject the proposals using the Metropolis Hasting criterion using the highest fidelity model which ensures that the proposed method is ergodic with respect to the highest fidelity density function. We apply the proposed method to three test cases including some well-known benchmarks to compare it with existing methods and show that multi-fidelity No-U-turn sampling outperforms other methods.

OriginalspracheEnglisch
TitelMonte Carlo and Quasi-Monte Carlo Methods - MCQMC 2022
Redakteure/-innenAicke Hinrichs, Friedrich Pillichshammer, Peter Kritzer
Herausgeber (Verlag)Springer
Seiten543-560
Seitenumfang18
ISBN (Print)9783031597619
DOIs
PublikationsstatusVeröffentlicht - 2024
Veranstaltung15th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2022 - Linz, Österreich
Dauer: 17 Juli 202222 Juli 2022

Publikationsreihe

NameSpringer Proceedings in Mathematics and Statistics
Band460
ISSN (Print)2194-1009
ISSN (elektronisch)2194-1017

Konferenz

Konferenz15th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2022
Land/GebietÖsterreich
OrtLinz
Zeitraum17/07/2222/07/22

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