Year: 2024
Type: preprint
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.
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funders: National Science Foundation, International Max Planck Research School for Environmental, Cellular and Molecular Microbiology, Deutsche Forschungsgemeinschaft, Bundesministerium für Bildung und Forschung, International Max Planck Research School for Advanced Methods in Process and Systems Engineering, Engineering and Physical Sciences Research Council, Division of Biological Infrastructure, H2020 European Research Council, HORIZON EUROPE European Research Council
Awards: G1562512020, Probabilistic Automated Numerical Analysis in Machine learning and Artificial intelligence, G2074461085, G442688124, Verbundprojekt TUEAI: Tübingen AI Center, G688259535, Advanced Numerics for Uncertainty and Bayesian Inference in Science, AI Institute for Artificial and Natural Intelligence, Unifying Probabilistic Computation for PDEs and Linear Systems, EXC 2064: Maschinelles Lernen: Neue Perspektiven für die Wissenschaft, G8556661049, G864726782
OpenAlex ID: W4396986729