Computation-Aware Kalman Filtering and Smoothing

Marvin Pförtner, Jonathan Wenger, Jon Cockayne, Philipp Hennig
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:2071-2079, 2025.

Abstract

Kalman filtering and smoothing are the foundational mechanisms for efficient inference in Gauss-Markov models. However, their time and memory complexities scale prohibitively with the size of the state space. This is particularly problematic in spatiotemporal regression problems, where the state dimension scales with the number of spatial observations. Existing approximate frameworks leverage low-rank approximations of the covariance matrix. But since they do not model the error introduced by the computational approximation, their predictive uncertainty estimates can be overly optimistic. In this work, we propose a probabilistic numerical method for inference in high-dimensional Gauss-Markov models which mitigates these scaling issues. Our matrix-free iterative algorithm leverages GPU acceleration and crucially enables a tunable trade-off between computational cost and predictive uncertainty. Finally, we demonstrate the scalability of our method on a large-scale climate dataset.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-pfortner25a, title = {Computation-Aware Kalman Filtering and Smoothing}, author = {Pf{\"o}rtner, Marvin and Wenger, Jonathan and Cockayne, Jon and Hennig, Philipp}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {2071--2079}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/pfortner25a/pfortner25a.pdf}, url = {https://proceedings.mlr.press/v258/pfortner25a.html}, abstract = {Kalman filtering and smoothing are the foundational mechanisms for efficient inference in Gauss-Markov models. However, their time and memory complexities scale prohibitively with the size of the state space. This is particularly problematic in spatiotemporal regression problems, where the state dimension scales with the number of spatial observations. Existing approximate frameworks leverage low-rank approximations of the covariance matrix. But since they do not model the error introduced by the computational approximation, their predictive uncertainty estimates can be overly optimistic. In this work, we propose a probabilistic numerical method for inference in high-dimensional Gauss-Markov models which mitigates these scaling issues. Our matrix-free iterative algorithm leverages GPU acceleration and crucially enables a tunable trade-off between computational cost and predictive uncertainty. Finally, we demonstrate the scalability of our method on a large-scale climate dataset.} }
Endnote
%0 Conference Paper %T Computation-Aware Kalman Filtering and Smoothing %A Marvin Pförtner %A Jonathan Wenger %A Jon Cockayne %A Philipp Hennig %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-pfortner25a %I PMLR %P 2071--2079 %U https://proceedings.mlr.press/v258/pfortner25a.html %V 258 %X Kalman filtering and smoothing are the foundational mechanisms for efficient inference in Gauss-Markov models. However, their time and memory complexities scale prohibitively with the size of the state space. This is particularly problematic in spatiotemporal regression problems, where the state dimension scales with the number of spatial observations. Existing approximate frameworks leverage low-rank approximations of the covariance matrix. But since they do not model the error introduced by the computational approximation, their predictive uncertainty estimates can be overly optimistic. In this work, we propose a probabilistic numerical method for inference in high-dimensional Gauss-Markov models which mitigates these scaling issues. Our matrix-free iterative algorithm leverages GPU acceleration and crucially enables a tunable trade-off between computational cost and predictive uncertainty. Finally, we demonstrate the scalability of our method on a large-scale climate dataset.
APA
Pförtner, M., Wenger, J., Cockayne, J. & Hennig, P.. (2025). Computation-Aware Kalman Filtering and Smoothing. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:2071-2079 Available from https://proceedings.mlr.press/v258/pfortner25a.html.

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