Année
2023
Auteurs
FULOP Andras, HENG Jeremy, CHOPIN Nicolas, THIERY Alexandre H.
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 htransforms 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 f ilters in the regime of highly informative observations, when the observations are extreme under the model, or if the state dimension is large.
CHOPIN, N., FULOP, A., HENG, J. et THIERY, A.H. (2023). Computational Doob h-transforms for Online Filtering of Discretely Observed Diffusions. Dans: Proceedings of the 40th International Conference on Machine Learning, PMLR 202:5904-5923. Honolulu: Proceedings of Machine Learning Research.