Bias of particle approximations to optimal filter derivative
In many applications, a state-space model depends on a parameter which needs to be inferred from data in an online manner. In the maximum likelihood approach, this can be achieved using stochastic gradient search, where the underlying gradient estimation is based on the optimal filter and the optima...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Society for Industrial and Applied Mathematics
2021
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| _version_ | 1797074482378047488 |
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| author | Tadic, VZB Doucet, A |
| author_facet | Tadic, VZB Doucet, A |
| author_sort | Tadic, VZB |
| collection | OXFORD |
| description | In many applications, a state-space model depends on a parameter which needs
to be inferred from data in an online manner. In the maximum likelihood approach, this can be
achieved using stochastic gradient search, where the underlying gradient estimation is based on the
optimal filter and the optimal filter derivative. However, the optimal filter and its derivative are not
analytically tractable for a non-linear state-space model and need to be approximated numerically. In
[22], a particle approximation to this derivative has been proposed, while the corresponding central
limit theorem and Lp error bounds have been established in [11]. We derive here bounds on the
bias of this particle approximation. Under mixing conditions, these bounds are uniform in time and
inversely proportional to the number of particles. |
| first_indexed | 2024-03-06T23:36:49Z |
| format | Journal article |
| id | oxford-uuid:6df24db1-9121-441a-924c-1befd8da64f2 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T23:36:49Z |
| publishDate | 2021 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:6df24db1-9121-441a-924c-1befd8da64f22022-03-26T19:21:09ZBias of particle approximations to optimal filter derivativeJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:6df24db1-9121-441a-924c-1befd8da64f2EnglishSymplectic ElementsSociety for Industrial and Applied Mathematics2021Tadic, VZBDoucet, AIn many applications, a state-space model depends on a parameter which needs to be inferred from data in an online manner. In the maximum likelihood approach, this can be achieved using stochastic gradient search, where the underlying gradient estimation is based on the optimal filter and the optimal filter derivative. However, the optimal filter and its derivative are not analytically tractable for a non-linear state-space model and need to be approximated numerically. In [22], a particle approximation to this derivative has been proposed, while the corresponding central limit theorem and Lp error bounds have been established in [11]. We derive here bounds on the bias of this particle approximation. Under mixing conditions, these bounds are uniform in time and inversely proportional to the number of particles. |
| spellingShingle | Tadic, VZB Doucet, A Bias of particle approximations to optimal filter derivative |
| title | Bias of particle approximations to optimal filter derivative |
| title_full | Bias of particle approximations to optimal filter derivative |
| title_fullStr | Bias of particle approximations to optimal filter derivative |
| title_full_unstemmed | Bias of particle approximations to optimal filter derivative |
| title_short | Bias of particle approximations to optimal filter derivative |
| title_sort | bias of particle approximations to optimal filter derivative |
| work_keys_str_mv | AT tadicvzb biasofparticleapproximationstooptimalfilterderivative AT douceta biasofparticleapproximationstooptimalfilterderivative |