dc.contributor.author Murray, LM dc.contributor.author Singh, Sumeetpal dc.contributor.author Lee, A dc.date.accessioned 2021-10-22T23:30:16Z dc.date.available 2021-10-22T23:30:16Z dc.date.issued 2021 dc.identifier.issn 2632-6736 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/329791 dc.description.abstract Abstract Monte Carlo algorithms simulates some prescribed number of samples, taking some random real time to complete the computations necessary. This work considers the converse: to impose a real-time budget on the computation, which results in the number of samples simulated being random. To complicate matters, the real time taken for each simulation may depend on the sample produced, so that the samples themselves are not independent of their number, and a length bias with respect to compute time is apparent. This is especially problematic when a Markov chain Monte Carlo (MCMC) algorithm is used and the final state of the Markov chain—rather than an average over all states—is required, which is the case in parallel tempering implementations of MCMC. The length bias does not diminish with the compute budget in this case. It also occurs in sequential Monte Carlo (SMC) algorithms, which is the focus of this paper. We propose an anytime framework to address the concern, using a continuous-time Markov jump process to study the progress of the computation in real time. We first show that for any MCMC algorithm, the length bias of the final state’s distribution due to the imposed real-time computing budget can be eliminated by using a multiple chain construction. The utility of this construction is then demonstrated on a large-scale SMC ${}^2$ implementation, using four billion particles distributed across a cluster of 128 graphics processing units on the Amazon EC2 service. The anytime framework imposes a real-time budget on the MCMC move steps within the SMC ${}^2$ algorithm, ensuring that all processors are simultaneously ready for the resampling step, demonstrably reducing idleness to due waiting times and providing substantial control over the total compute budget. dc.language en dc.publisher Cambridge University Press (CUP) dc.rights Attribution 4.0 International dc.rights.uri https://creativecommons.org/licenses/by/4.0/ dc.title Anytime Monte Carlo dc.type Article prism.number e7 prism.publicationDate 2021 prism.publicationName Data-Centric Engineering prism.volume 2 dc.identifier.doi 10.17863/CAM.77236 rioxxterms.versionofrecord 10.1017/dce.2021.6 rioxxterms.version VoR rioxxterms.licenseref.uri http://www.rioxx.net/licenses/all-rights-reserved rioxxterms.licenseref.startdate 2021 dc.contributor.orcid Singh, Sumeetpal [0000-0002-5430-1496] dc.identifier.eissn 2632-6736 rioxxterms.type Journal Article/Review pubs.funder-project-id Alan Turing Institute (unknown) cam.issuedOnline 2021-06-29
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Except where otherwise noted, this item's licence is described as Attribution 4.0 International