A Stochastic Approximation-Langevinized Ensemble Kalman Filter Algorithm for State Space Models with Unknown Parameters Article Swipe
Tianning Dong
,
Peiyi Zhang
,
Faming Liang
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.6084/m9.figshare.20405677
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.6084/m9.figshare.20405677
Inference for high-dimensional, large scale and long series dynamic systems is a challenging task in modern data science. The existing algorithms, such as particle filter or sequential importance sampler, do not scale well to the dimension of the system and the sample size of the dataset, and often suffers from the sample degeneracy issue for long series data. The recently proposed Langevinized ensemble Kalman filter (LEnKF) addresses these difficulties in a coherent way. However, it cannot be applied to the case that the dynamic system contains unknown parameters. This article proposes the so-called stochastic approximation-LEnKF for jointly estimating the states and unknown parameters of the dynamic system, where the parameters are estimated on the fly based on the state variables simulated by the LEnKF under the framework of stochastic approximation Markov chain Monte Carlo (MCMC). Under mild conditions, we prove its consistency in parameter estimation and ergodicity in state variable simulations. The proposed algorithm can be used in uncertainty quantification for long series, large scale, and high-dimensional dynamic systems. Numerical results indicate its superiority over the existing algorithms. We employ the proposed algorithm in state-space modeling of the sea surface temperature with a long short term memory (LSTM) network, which indicates its great potential in statistical analysis of complex dynamic systems encountered in modern data science. Supplementary materials for this article are available online.
Related Topics
Concepts
Kalman filter
Ensemble Kalman filter
State space
State-space representation
Algorithm
Fast Kalman filter
Extended Kalman filter
Computer science
Alpha beta filter
State (computer science)
Moving horizon estimation
Space (punctuation)
Mathematics
Artificial intelligence
Statistics
Operating system
Metadata
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- Language
- en
- Landing Page
- https://doi.org/10.6084/m9.figshare.20405677
- OA Status
- gold
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- OpenAlex ID
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https://openalex.org/W4394318179Canonical identifier for this work in OpenAlex
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https://doi.org/10.6084/m9.figshare.20405677Digital Object Identifier
- Title
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A Stochastic Approximation-Langevinized Ensemble Kalman Filter Algorithm for State Space Models with Unknown ParametersWork title
- Type
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datasetOpenAlex work type
- Language
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enPrimary language
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2022Year of publication
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2022-01-01Full publication date if available
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Tianning Dong, Peiyi Zhang, Faming LiangList of authors in order
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https://doi.org/10.6084/m9.figshare.20405677Publisher landing page
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YesWhether a free full text is available
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goldOpen access status per OpenAlex
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https://doi.org/10.6084/m9.figshare.20405677Direct OA link when available
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Kalman filter, Ensemble Kalman filter, State space, State-space representation, Algorithm, Fast Kalman filter, Extended Kalman filter, Computer science, Alpha beta filter, State (computer science), Moving horizon estimation, Space (punctuation), Mathematics, Artificial intelligence, Statistics, Operating systemTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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