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dc.contributor.authorRuzayqat, Hamza Mahmoud
dc.contributor.authorEr-raiy, Aimad
dc.contributor.authorBeskos, Alexandros
dc.contributor.authorCrisan, Dan
dc.contributor.authorJasra, Ajay
dc.contributor.authorKantas, Nikolas
dc.date.accessioned2021-10-06T06:11:14Z
dc.date.available2021-10-06T06:11:14Z
dc.date.issued2021-10-02
dc.identifier.urihttp://hdl.handle.net/10754/672163
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 $d\rightarrow\infty$ the cost to achieve a stable mean square error in estimation, for classes of expectations, is of $\mathcal{O}(Nd^2)$ 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.
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.
dc.publisherarXiv
dc.relation.urlhttps://arxiv.org/pdf/2110.00884.pdf
dc.rightsArchived with thanks to arXiv
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.titleA Lagged Particle Filter for Stable Filtering of certain High-Dimensional State-Space Models
dc.typePreprint
dc.contributor.departmentComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
dc.eprint.versionPre-print
dc.contributor.institutionDepartment of Statistical Science, University College London, London, WC1E 6BT, UK.
dc.contributor.institutionDepartment of Mathematics, Imperial College London, London, SW7 2AZ, UK.
dc.identifier.arxivid2110.00884
kaust.personRuzayqat, Hamza Mahmoud
kaust.personEr-Raiy, Aimad
kaust.personJasra, Ajay
refterms.dateFOA2021-10-06T06:13:24Z
kaust.acknowledged.supportUnitKAUST baseline funding


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