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    Score-Based Parameter Estimation for a Class of Continuous-Time State Space Models

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    Type
    Preprint
    Authors
    Beskos, Alexandros
    Crisan, Dan
    Jasra, Ajay cc
    Kantas, Nikolas
    Ruzayqat, Hamza
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2020-08-18
    Permanent link to this record
    http://hdl.handle.net/10754/664791
    
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    Abstract
    We consider the problem of parameter estimation for a class of continuous-time state space models. 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 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.
    Publisher
    arXiv
    arXiv
    2008.07803
    Additional Links
    https://arxiv.org/pdf/2008.07803
    Collections
    Preprints; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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