Nonlinear Filtering with Brenier Optimal Transport Maps

Mohammad Al-Jarrah, Niyizhen Jin, Bamdad Hosseini, Amirhossein Taghvaei
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:813-839, 2024.

Abstract

This paper is concerned with the problem of nonlinear filtering, i.e., computing the conditional distribution of the state of a stochastic dynamical system given a history of noisy partial observations. Conventional sequential importance resampling (SIR) particle filters suffer from fundamental limitations, in scenarios involving degenerate likelihoods or high-dimensional states, due to the weight degeneracy issue. In this paper, we explore an alternative method, which is based on estimating the Brenier optimal transport (OT) map from the current prior distribution of the state to the posterior distribution at the next time step. Unlike SIR particle filters, the OT formulation does not require the analytical form of the likelihood. Moreover, it allows us to harness the approximation power of neural networks to model complex and multi-modal distributions and employ stochastic optimization algorithms to enhance scalability. Extensive numerical experiments are presented that compare the OT method to the SIR particle filter and the ensemble Kalman filter, evaluating the performance in terms of sample efficiency, high-dimensional scalability, and the ability to capture complex and multi-modal distributions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-al-jarrah24a, title = {Nonlinear Filtering with Brenier Optimal Transport Maps}, author = {Al-Jarrah, Mohammad and Jin, Niyizhen and Hosseini, Bamdad and Taghvaei, Amirhossein}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {813--839}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/al-jarrah24a/al-jarrah24a.pdf}, url = {https://proceedings.mlr.press/v235/al-jarrah24a.html}, abstract = {This paper is concerned with the problem of nonlinear filtering, i.e., computing the conditional distribution of the state of a stochastic dynamical system given a history of noisy partial observations. Conventional sequential importance resampling (SIR) particle filters suffer from fundamental limitations, in scenarios involving degenerate likelihoods or high-dimensional states, due to the weight degeneracy issue. In this paper, we explore an alternative method, which is based on estimating the Brenier optimal transport (OT) map from the current prior distribution of the state to the posterior distribution at the next time step. Unlike SIR particle filters, the OT formulation does not require the analytical form of the likelihood. Moreover, it allows us to harness the approximation power of neural networks to model complex and multi-modal distributions and employ stochastic optimization algorithms to enhance scalability. Extensive numerical experiments are presented that compare the OT method to the SIR particle filter and the ensemble Kalman filter, evaluating the performance in terms of sample efficiency, high-dimensional scalability, and the ability to capture complex and multi-modal distributions.} }
Endnote
%0 Conference Paper %T Nonlinear Filtering with Brenier Optimal Transport Maps %A Mohammad Al-Jarrah %A Niyizhen Jin %A Bamdad Hosseini %A Amirhossein Taghvaei %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-al-jarrah24a %I PMLR %P 813--839 %U https://proceedings.mlr.press/v235/al-jarrah24a.html %V 235 %X This paper is concerned with the problem of nonlinear filtering, i.e., computing the conditional distribution of the state of a stochastic dynamical system given a history of noisy partial observations. Conventional sequential importance resampling (SIR) particle filters suffer from fundamental limitations, in scenarios involving degenerate likelihoods or high-dimensional states, due to the weight degeneracy issue. In this paper, we explore an alternative method, which is based on estimating the Brenier optimal transport (OT) map from the current prior distribution of the state to the posterior distribution at the next time step. Unlike SIR particle filters, the OT formulation does not require the analytical form of the likelihood. Moreover, it allows us to harness the approximation power of neural networks to model complex and multi-modal distributions and employ stochastic optimization algorithms to enhance scalability. Extensive numerical experiments are presented that compare the OT method to the SIR particle filter and the ensemble Kalman filter, evaluating the performance in terms of sample efficiency, high-dimensional scalability, and the ability to capture complex and multi-modal distributions.
APA
Al-Jarrah, M., Jin, N., Hosseini, B. & Taghvaei, A.. (2024). Nonlinear Filtering with Brenier Optimal Transport Maps. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:813-839 Available from https://proceedings.mlr.press/v235/al-jarrah24a.html.

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