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dc.contributor.authorHoussineau, Jeremie
dc.contributor.authorJasra, Ajay
dc.contributor.authorSingh, Sumeetpal S.
dc.date.accessioned2020-01-13T07:56:02Z
dc.date.available2020-01-13T07:56:02Z
dc.date.issued2019-12-03
dc.identifier.citationHoussineau, J., Jasra, A., & Singh, S. S. (2019). On Large Lag Smoothing for Hidden Markov Models. SIAM Journal on Numerical Analysis, 57(6), 2812–2828. doi:10.1137/18m1198004
dc.identifier.doi10.1137/18M1198004
dc.identifier.urihttp://hdl.handle.net/10754/660989.1
dc.description.abstractIn this article we consider the smoothing problem for hidden Markov models. Given a hidden Markov chain { Xn} n≥ 0 and observations { Yn} n≥ 0, our objective is to compute E[varphi (X0, . ,Xk)| y0, . , yn] for some real-valued, integrable functional varphi and k fixed, k ll n and for some realization (y0, . , yn) of (Y0, . , Yn). We introduce a novel application of the multilevel Monte Carlo method with a coupling based on the Knothe-Rosenblatt rearrangement. We prove that this method can approximate the aforementioned quantity with a mean square error (MSE) of scrO (∈-2) for arbitrary ∈ > 0 with a cost of scrO (∈-2). This is in contrast to the same direct Monte Carlo method, which requires a cost of scrO (n∈-2) for the same MSE. The approach we suggest is, in general, not possible to implement, so the optimal transport methodology of [A. Spantini, D. Bigoni, and Y. Marzouk, J. Mach. Learn. Res., 19 (2018), pp. 2639-2709; M. Parno, T. Moselhy, and Y. Marzouk, SIAM/ASA J. Uncertain. Quantif., 4 (2016), pp. 1160-1190] is used, which directly approximates our strategy. We show that our theoretical improvements are achieved, even under approximation, in several numerical examples.
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.relation.urlhttps://epubs.siam.org/doi/10.1137/18M1198004
dc.relation.urlhttp://arxiv.org/pdf/1804.07117
dc.rightsArchived with thanks to SIAM Journal on Numerical Analysis
dc.titleOn large lag smoothing for hidden markov models
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalSIAM Journal on Numerical Analysis
dc.eprint.versionPost-print
dc.contributor.institutionDepartment of Statistics, University of Warwick, Coventry, CV4 7AL, UK
dc.contributor.institutionDepartment of Engineering, University of Cambridge, Alan Turing Institute, Cambridge, CB2 1PZ, UK
dc.identifier.arxivid1804.07117
kaust.personJasra, Ajay
refterms.dateFOA2020-01-13T08:04:47Z
dc.date.published-online2019-12-03
dc.date.published-print2019-01


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