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Approximate smoothing and parameter estimation in high-dimensional state-space models

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posted on 2020-08-24, 10:03 authored by Axel FinkeAxel Finke, Sumeetpal S. Singh
We 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 Processing

Volume

65

Issue

22

Pages

5982 - 5994

Publisher

IEEE

Version

  • AM (Accepted Manuscript)

Rights holder

© IEEE

Publisher 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

2017-07-10

Publication date

2017-08-09

Copyright date

2017

ISSN

1053-587X

eISSN

1941-0476

Language

  • en

Depositor

Axel Finke. Deposit date: 22 August 2020

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