dc.contributor.author Beskos, Alexandros dc.contributor.author Crisan, Dan dc.contributor.author Jasra, Ajay dc.contributor.author Kantas, Nikolas dc.contributor.author Ruzayqat, Hamza Mahmoud dc.date.accessioned 2021-08-04T12:16:25Z dc.date.available 2020-08-24T10:08:16Z dc.date.available 2021-08-04T12:16:25Z dc.date.issued 2021-07-15 dc.identifier.citation Beskos, A., Crisan, D., Jasra, A., Kantas, N., & Ruzayqat, H. (2021). Score-Based Parameter Estimation for a Class of Continuous-Time State Space Models. SIAM Journal on Scientific Computing, 43(4), A2555–A2580. doi:10.1137/20m1362942 dc.identifier.issn 1064-8275 dc.identifier.issn 1095-7197 dc.identifier.doi 10.1137/20m1362942 dc.identifier.uri http://hdl.handle.net/10754/664791 dc.description.abstract We consider the problem of parameter estimation for a class of continuous-time state space models (SSMs). In particular, we explore the case of a partially observed diffusion, with data also arriving according to a diffusion process. Based upon a standard identity of the score function, we consider two particle filter based methodologies to estimate the score function. Both methods rely on an online estimation algorithm for the score function, as described, e.g., in [P. Del Moral, A. Doucet, and S. S. Singh, M$2$AN Math. Model. Numer. Anal., 44 (2010), pp. 947--975], of $\mathcal{O}(N^2)$ cost, with $N\in\mathbb{N}$ the number of particles. The first approach employs a simple Euler discretization and standard particle smoothers and is of cost $\mathcal{O}(N^2 + N\Delta_l^{-1})$ per unit time, where $\Delta_l=2^{-l}$, $l\in\mathbb{N}_0$, is the time-discretization step. The second approach is new and based upon a novel diffusion bridge construction. It yields a new backward-type Feynman--Kac formula in continuous time for the score function and is presented along with a particle method for its approximation. Considering a time-discretization, the cost is $\mathcal{O}(N^2\Delta_l^{-1})$ per unit time. To improve computational costs, we then consider multilevel methodologies for the score function. We illustrate our parameter estimation method via stochastic gradient approaches in several numerical examples. dc.description.sponsorship The work of the third and fifth authors was supported by KAUST baseline funding. The work of the first author was supported by a Leverhulme Trust Prize. The work of the second author was partially supported by EU Synergy project STUOD - DLV-856408. The work of the fourth author was supported by a JP Morgan A.I. Faculty award. dc.publisher Society for Industrial & Applied Mathematics (SIAM) dc.relation.url https://epubs.siam.org/doi/10.1137/20M1362942 dc.rights Archived with thanks to SIAM Journal on Scientific Computing dc.title Score-Based Parameter Estimation for a Class of Continuous-Time State Space Models dc.type Article dc.contributor.department Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division dc.identifier.journal SIAM Journal on Scientific Computing dc.eprint.version Publisher's Version/PDF 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.volume 43 dc.identifier.issue 4 dc.identifier.pages A2555-A2580 dc.identifier.arxivid 2008.07803 kaust.person Jasra, Ajay kaust.person Ruzayqat, Hamza Mahmoud refterms.dateFOA 2020-08-24T10:09:43Z kaust.acknowledged.supportUnit KAUST baseline funding
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