Scalable Optimization-Based Sampling on Function Space
Name
19m1245220.pdf
Description
Published version
Size
1.99 MB
Format
Adobe PDF
Checksum (MD5)
280f66d6f8e9fb6cb077f5219dfa7f74
Author(s)
Bardsley, Johnathan M
Cui, Tiangang
Marzouk, Youssef M
Wang, Zheng
Date Issued
2020
Journal
SIAM Journal on Scientific Computing
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Version
Final published version
Abstract
© 2020 Society for Industrial and Applied Mathematics. Optimization-based samplers such as randomize-then-optimize (RTO) [J. M. Bardsley et al., SIAM J. Sci. Comput., 36 (2014), pp. A1895-A1910] provide an efficient and parallellizable approach to solving large-scale Bayesian inverse problems. These methods solve randomly perturbed optimization problems to draw samples from an approximate posterior distribution. "Correcting" these samples, either by Metropolization or importance sampling, enables characterization of the original posterior distribution. This paper focuses on the scalability of RTO to problems with highor infinite-dimensional parameters. In particular, we introduce a new subspace strategy to reformulate RTO. For problems with intrinsic low-rank structures, this subspace acceleration makes the computational complexity of RTO scale linearly with the parameter dimension. Furthermore, this subspace perspective suggests a natural extension of RTO to a function space setting. We thus formalize a function space version of RTO and establish sufficient conditions for it to produce a valid Metropolis-Hastings proposal, yielding dimension-independent sampling performance. Numerical examples corroborate the dimension independence of RTO and demonstrate sampling performance that is also robust to small observational noise.
MIT Department
Massachusetts Institute of Technology. Center for Computational Engineering
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DOI of Published Version
https://doi.org/10.1137/19M1245220
