Markovian stochastic approximation with expanding projections
Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be unstable without additional stabilisation techniques. We stu...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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International Statistical Institute
2014
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| _version_ | 1797054444692570112 |
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| author | Andrieu, C Vihola, M |
| author_facet | Andrieu, C Vihola, M |
| author_sort | Andrieu, C |
| collection | OXFORD |
| description | Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be unstable without additional stabilisation techniques. We study a stochastic approximation procedure with expanding projections similar to Andradóttir [Oper. Res. 43 (1995) 1037-1048]. We focus on Markovian noise and show the stability and convergence under general conditions. Our framework also incorporates the possibility to use a random step size sequence, which allows us to consider settings with a non-smooth family of Markov kernels. We apply the theory to stochastic approximation expectation maximisation with particle independent Metropolis-Hastings sampling. © 2014 ISI/BS. |
| first_indexed | 2024-03-06T18:57:23Z |
| format | Journal article |
| id | oxford-uuid:124f47c7-94ac-4d6f-9435-abc6db1628ba |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T18:57:23Z |
| publishDate | 2014 |
| publisher | International Statistical Institute |
| record_format | dspace |
| spelling | oxford-uuid:124f47c7-94ac-4d6f-9435-abc6db1628ba2022-03-26T10:07:12ZMarkovian stochastic approximation with expanding projectionsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:124f47c7-94ac-4d6f-9435-abc6db1628baEnglishSymplectic Elements at OxfordInternational Statistical Institute2014Andrieu, CVihola, MStochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be unstable without additional stabilisation techniques. We study a stochastic approximation procedure with expanding projections similar to Andradóttir [Oper. Res. 43 (1995) 1037-1048]. We focus on Markovian noise and show the stability and convergence under general conditions. Our framework also incorporates the possibility to use a random step size sequence, which allows us to consider settings with a non-smooth family of Markov kernels. We apply the theory to stochastic approximation expectation maximisation with particle independent Metropolis-Hastings sampling. © 2014 ISI/BS. |
| spellingShingle | Andrieu, C Vihola, M Markovian stochastic approximation with expanding projections |
| title | Markovian stochastic approximation with expanding projections |
| title_full | Markovian stochastic approximation with expanding projections |
| title_fullStr | Markovian stochastic approximation with expanding projections |
| title_full_unstemmed | Markovian stochastic approximation with expanding projections |
| title_short | Markovian stochastic approximation with expanding projections |
| title_sort | markovian stochastic approximation with expanding projections |
| work_keys_str_mv | AT andrieuc markovianstochasticapproximationwithexpandingprojections AT viholam markovianstochasticapproximationwithexpandingprojections |