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dc.contributor.authorHoussineau, Jen
dc.contributor.authorJasra, Aen
dc.contributor.authorSingh, Sumeetpalen
dc.date.accessioned2019-09-04T23:30:45Z
dc.date.available2019-09-04T23:30:45Z
dc.date.issued2019-01-01en
dc.identifier.issn0036-1429
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/296419
dc.description.abstractIn this article we consider the smoothing problem for hidden Markov models (HMM). Given a hidden Markov chain $\{X_n\}_{n\geq 0}$ and observations $\{Y_n\}_{n\geq 0}$, our objective is to compute $\mathbb{E}[\varphi(X_0,\dots,X_k)|y_{0},\dots,y_n]$ for some real-valued, integrable functional $\varphi$ and $k$ fixed, $k \ll n$ and for some realisation $(y_0,\dots,y_n)$ of $(Y_0,\dots,Y_n)$. We introduce a novel application of the multilevel Monte Carlo (MLMC) method with a coupling based on the Knothe-Rosenblatt rearrangement. We prove that this method can approximate the afore-mentioned quantity with a mean square error (MSE) of $\mathcal{O}(\epsilon^2)$, for arbitrary $\epsilon>0$ with a cost of $\mathcal{O}(\epsilon^{-2})$. This is in contrast to the same direct Monte Carlo method, which requires a cost of $\mathcal{O}(n\epsilon^{-2})$ for the same MSE. The approach we suggest is, in general, not possible to implement, so the optimal transport methodology of \cite{span, parno} 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 and Applied Mathematics
dc.rightsAll rights reserved
dc.rights.uri
dc.titleOn large lag smoothing for hidden markov modelsen
dc.typeArticle
prism.endingPage2828
prism.issueIdentifier6en
prism.publicationDate2019en
prism.publicationNameSIAM Journal on Numerical Analysisen
prism.startingPage2812
prism.volume57en
dc.identifier.doi10.17863/CAM.43469
dcterms.dateAccepted2019-08-30en
rioxxterms.versionofrecord10.1137/18M1198004en
rioxxterms.versionAM
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.licenseref.startdate2019-01-01en
dc.identifier.eissn1095-7170
rioxxterms.typeJournal Article/Reviewen
pubs.funder-project-idAlan Turing Institute (unknown)
cam.orpheus.successThu Jan 30 10:40:58 GMT 2020 - Embargo updated*
rioxxterms.freetoread.startdate2019-01-01


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