dc.contributor.author Ruzayqat, Hamza Mahmoud dc.contributor.author Er-raiy, Aimad dc.contributor.author Beskos, Alexandros dc.contributor.author Crisan, Dan dc.contributor.author Jasra, Ajay dc.contributor.author Kantas, Nikolas dc.date.accessioned 2021-10-06T06:11:14Z dc.date.available 2021-10-06T06:11:14Z dc.date.issued 2021-10-02 dc.identifier.uri http://hdl.handle.net/10754/672163 dc.description.abstract We 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.sponsorship AJ & 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.publisher arXiv dc.relation.url https://arxiv.org/pdf/2110.00884.pdf dc.rights Archived with thanks to arXiv dc.rights.uri http://creativecommons.org/licenses/by/4.0/ dc.title A Lagged Particle Filter for Stable Filtering of certain High-Dimensional State-Space Models dc.type Preprint dc.contributor.department Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division dc.eprint.version Pre-print dc.contributor.institution Department of Statistical Science, University College London, London, WC1E 6BT, UK. dc.contributor.institution Department of Mathematics, Imperial College London, London, SW7 2AZ, UK. dc.identifier.arxivid 2110.00884 kaust.person Ruzayqat, Hamza Mahmoud kaust.person Er-Raiy, Aimad kaust.person Jasra, Ajay refterms.dateFOA 2021-10-06T06:13:24Z kaust.acknowledged.supportUnit KAUST baseline funding
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