Computational Doob h-transforms for Online Filtering of Discretely Observed Diffusions

Nicolas Chopin, Andras Fulop, Jeremy Heng, Alexandre H. Thiery
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:5904-5923, 2023.

Abstract

This paper is concerned with online filtering of discretely observed nonlinear diffusion processes. Our approach is based on the fully adapted auxiliary particle filter, which involves Doob’s $h$-transforms that are typically intractable. We propose a computational framework to approximate these $h$-transforms by solving the underlying backward Kolmogorov equations using nonlinear Feynman-Kac formulas and neural networks. The methodology allows one to train a locally optimal particle filter prior to the data-assimilation procedure. Numerical experiments illustrate that the proposed approach can be orders of magnitude more efficient than state-of-the-art particle filters in the regime of highly informative observations, when the observations are extreme under the model, and if the state dimension is large.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-chopin23a, title = {Computational Doob h-transforms for Online Filtering of Discretely Observed Diffusions}, author = {Chopin, Nicolas and Fulop, Andras and Heng, Jeremy and Thiery, Alexandre H.}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {5904--5923}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/chopin23a/chopin23a.pdf}, url = {https://proceedings.mlr.press/v202/chopin23a.html}, abstract = {This paper is concerned with online filtering of discretely observed nonlinear diffusion processes. Our approach is based on the fully adapted auxiliary particle filter, which involves Doob’s $h$-transforms that are typically intractable. We propose a computational framework to approximate these $h$-transforms by solving the underlying backward Kolmogorov equations using nonlinear Feynman-Kac formulas and neural networks. The methodology allows one to train a locally optimal particle filter prior to the data-assimilation procedure. Numerical experiments illustrate that the proposed approach can be orders of magnitude more efficient than state-of-the-art particle filters in the regime of highly informative observations, when the observations are extreme under the model, and if the state dimension is large.} }
Endnote
%0 Conference Paper %T Computational Doob h-transforms for Online Filtering of Discretely Observed Diffusions %A Nicolas Chopin %A Andras Fulop %A Jeremy Heng %A Alexandre H. Thiery %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-chopin23a %I PMLR %P 5904--5923 %U https://proceedings.mlr.press/v202/chopin23a.html %V 202 %X This paper is concerned with online filtering of discretely observed nonlinear diffusion processes. Our approach is based on the fully adapted auxiliary particle filter, which involves Doob’s $h$-transforms that are typically intractable. We propose a computational framework to approximate these $h$-transforms by solving the underlying backward Kolmogorov equations using nonlinear Feynman-Kac formulas and neural networks. The methodology allows one to train a locally optimal particle filter prior to the data-assimilation procedure. Numerical experiments illustrate that the proposed approach can be orders of magnitude more efficient than state-of-the-art particle filters in the regime of highly informative observations, when the observations are extreme under the model, and if the state dimension is large.
APA
Chopin, N., Fulop, A., Heng, J. & Thiery, A.H.. (2023). Computational Doob h-transforms for Online Filtering of Discretely Observed Diffusions. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:5904-5923 Available from https://proceedings.mlr.press/v202/chopin23a.html.

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