Ensemble Markov Chain Monte Carlo with Teleporting Walkers
Abstract.
We introduce an ensemble Markov chain Monte Carlo approach to sampling from a probability density with known likelihood. This method upgrades an underlying Markov chain by allowing an ensemble of such chains to interact via a process in which one chain’s state is cloned as another’s is deleted. This effective teleportation of states can overcome issues of metastability in the underlying chain, as the scheme enjoys rapid mixing once the modes of the target density have been populated. We derive a mean-field limit for the evolution of the ensemble. We analyze the global and local convergence of this mean-field limit, showing asymptotic convergence independent of the spectral gap of the underlying Markov chain, and moreover we interpret the limiting evolution as a gradient flow. We explain how interaction can be applied selectively to a subset of state variables in order to maintain advantage on very high-dimensional problems. Finally, we present the application of our methodology to Bayesian hyperparameter estimation for Gaussian process regression.
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Information & Authors
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Published In
SIAM/ASA Journal on Uncertainty Quantification
Pages: 860 - 885
DOI: 10.1137/21M1425062
ISSN (online): 2166-2525
Copyright
© 2022 Society for Industrial and Applied Mathematics and American Statistical Association.
History
Submitted: 7 June 2021
Accepted: 8 February 2022
Published online: 29 July 2022
Keywords
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Authors
Funding Information
National Science Foundation (NSF): 1903031
U.S. Department of Energy (DOE): DE-SC0020427
The work of the first author was supported by National Science Foundation award 1903031. The work of the second author was supported by the Advanced Scientific Computing Research Program within the DOE Office of Science through award DE-SC0020427.
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