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Approximate smoothing and parameter estimation in high-dimensional state-space models
journal contribution
posted on 2020-08-24, 10:03 authored by Axel FinkeAxel Finke, Sumeetpal S. SinghWe present approximate algorithms for performing smoothing in a class of high-dimensional state-space models via sequential Monte Carlo methods (particle filters). In high dimensions, a prohibitively large number of Monte Carlo samples (particles), growing exponentially in the dimension of the state space, are usually required to obtain a useful smoother. Employing blocking approximations, we exploit the spatial ergodicity properties of the model to circumvent this curse of dimensionality. We thus obtain approximate smoothers that can be computed recursively in time and parallel in space. First, we show that the bias of our blocked smoother is bounded uniformly in the time horizon and in the model dimension. We then approximate the blocked smoother with particles and derive the asymptotic variance of idealized versions of our blocked particle smoother to show that variance is no longer adversely effected by the dimension of the model. Finally, we employ our method to successfully perform maximum-likelihood estimation via stochastic gradient-ascent and stochastic expectation-maximization algorithms in a 100-dimensional state-space model.
Funding
Engineering and Physical Sciences Research Council under Grant EP/K020153/1.
History
School
- Science
Department
- Mathematical Sciences
Published in
IEEE Transactions on Signal ProcessingVolume
65Issue
22Pages
5982 - 5994Publisher
IEEEVersion
- AM (Accepted Manuscript)
Rights holder
© IEEEPublisher statement
© 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Acceptance date
2017-07-10Publication date
2017-08-09Copyright date
2017ISSN
1053-587XeISSN
1941-0476Publisher version
Language
- en