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dc.contributor.authorRuzayqat, Hamza
dc.contributor.authorEr-raiy, Aimad
dc.contributor.authorBeskos, Alexandros
dc.contributor.authorCrisan, Dan
dc.contributor.authorJasra, Ajay
dc.contributor.authorKantas, Nikolas
dc.date.accessioned2021-10-10T05:37:37Z
dc.date.available2021-10-10T05:37:37Z
dc.date.issued2021-10-02
dc.identifier.urihttp://hdl.handle.net/10754/672458
dc.description.abstractWe consider the problem of high-dimensional filtering of state-space models (SSMs) at discrete times. This problem is particularly challenging as analytical solutions are typically not available and many numerical approximation methods can have a cost that scales exponentially with the dimension of the hidden state. Inspired by lag-approximation methods for the smoothing problem, we introduce a lagged approximation of the smoothing distribution that is necessarily biased. For certain classes of SSMs, particularly those that forget the initial condition exponentially fast in time, the bias of our approximation is shown to be uniformly controlled in the dimension and exponentially small in time. We develop a sequential Monte Carlo (SMC) method to recursively estimate expectations with respect to our biased filtering distributions. Moreover, we prove for a class of non-i.i.d.~SSMs that as the dimension d→∞ the cost to achieve a stable mean square error in estimation, for classes of expectations, is of O(N*d^2) per-unit time, where N is the number of simulated samples in the SMC algorithm. Our methodology is implemented on several challenging high-dimensional examples including the conservative shallow-water model.en_US
dc.description.sponsorshipAJ & HR were supported by KAUST baseline funding. The work of DC has been partially supported by European Research Council (ERC) Synergy grant STUOD-DLV-8564. NK was supported by a J.P. Morgan A.I. Research Award.en_US
dc.publisherarXiven_US
dc.relation.urlhttps://arxiv.org/pdf/2110.00884.pdfen_US
dc.subjectFiltering, Sequential Monte Carlo, Lag Approximations, High-Dimensional Particle Filteren_US
dc.titleA Lagged Particle Filter for Stable Filtering of certain High-Dimensional State-Space Modelsen_US
dc.typePreprint
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering Divisionen_US
dc.contributor.institutionImperial College Londonen_US
dc.contributor.institutionUniversity College Londonen_US
dc.identifier.arxivid2110.00884
refterms.dateFOA2021-10-08T00:00:00Z
display.summary<p>This record has been merged with an existing record at: <a href="http://hdl.handle.net/10754/672163">http://hdl.handle.net/10754/672163</a>.</p>


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