Nonlinear Bayesian Update via Ensemble Kernel Regression with Clustering and Subsampling
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908275178471424 |
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| author | Lee, Yoonsang |
| author_facet | Lee, Yoonsang |
| contents | Nonlinear Bayesian update for a prior ensemble is proposed to extend traditional ensemble Kalman filtering to settings characterized by non-Gaussian priors and nonlinear measurement operators. In this framework, the observed component is first denoised via a standard Kalman update, while the unobserved component is estimated using a nonlinear regression approach based on kernel density estimation. The method incorporates a subsampling strategy to ensure stability and, when necessary, employs unsupervised clustering to refine the conditional estimate. Numerical experiments on Lorenz systems and a PDE-constrained inverse problem illustrate that the proposed nonlinear update can reduce estimation errors compared to standard linear updates, especially in highly nonlinear scenarios. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_15160 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlinear Bayesian Update via Ensemble Kernel Regression with Clustering and Subsampling Lee, Yoonsang Machine Learning Probability Statistics Theory Nonlinear Bayesian update for a prior ensemble is proposed to extend traditional ensemble Kalman filtering to settings characterized by non-Gaussian priors and nonlinear measurement operators. In this framework, the observed component is first denoised via a standard Kalman update, while the unobserved component is estimated using a nonlinear regression approach based on kernel density estimation. The method incorporates a subsampling strategy to ensure stability and, when necessary, employs unsupervised clustering to refine the conditional estimate. Numerical experiments on Lorenz systems and a PDE-constrained inverse problem illustrate that the proposed nonlinear update can reduce estimation errors compared to standard linear updates, especially in highly nonlinear scenarios. |
| title | Nonlinear Bayesian Update via Ensemble Kernel Regression with Clustering and Subsampling |
| topic | Machine Learning Probability Statistics Theory |
| url | https://arxiv.org/abs/2503.15160 |