Computation-Aware Kalman Filtering and Smoothing

TL;DR

This paper introduces a scalable, GPU-accelerated probabilistic numerical method for Kalman filtering and smoothing in high-dimensional Gauss-Markov models, balancing computational efficiency with uncertainty quantification.

Contribution

It presents a matrix-free iterative algorithm that reduces complexity and models approximation errors, enabling scalable inference with uncertainty estimates.

Findings

Successfully applied to large-scale climate data

Achieves tunable trade-off between cost and uncertainty

Demonstrates improved scalability over existing methods

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.