# Computation-Aware Kalman Filtering and Smoothing

arXiv: https://arxiv.org/abs/2405.08971 · HTML: https://mlsanity.com/paper/2405.08971/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 53 references that are in the map.
- First posted on arXiv 14 May 2024.

## Builds on (most cited first, 14 of 14)

- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences](https://mlsanity.com/paper/1807.02582/) (2018)
- [Efficiently Sampling Functions from Gaussian Process Posteriors](https://mlsanity.com/paper/2002.09309/) (2020)
- [Probabilistic Numerics and Uncertainty in Computations](https://mlsanity.com/paper/1506.01326/) (2015)
- [Bayesian Probabilistic Numerical Methods](https://mlsanity.com/paper/1702.03673/) (2017)
- [Temporal Parallelization of Bayesian Smoothers](https://mlsanity.com/paper/1905.13002/) (2019)
- [Spatio-Temporal Variational Gaussian Processes](https://mlsanity.com/paper/2111.01732/) (2021)
- [Fast Matrix Square Roots with Applications to Gaussian Processes and Bayesian Optimization](https://mlsanity.com/paper/2006.11267/) (2020)
- [Posterior and Computational Uncertainty in Gaussian Processes](https://mlsanity.com/paper/2205.15449/) (2022)
- [Probabilistic Interpretation of Linear Solvers](https://mlsanity.com/paper/1402.2058/) (2014)
- [Probabilistic Linear Solvers for Machine Learning](https://mlsanity.com/paper/2010.09691/) (2020)
- [Efficient Spatio-Temporal Gaussian Regression via Kalman Filtering](https://mlsanity.com/paper/1705.01485/) (2017)
- [The Rank-Reduced Kalman Filter: Approximate Dynamical-Low-Rank Filtering In High Dimensions](https://mlsanity.com/paper/2306.07774/) (2023)
- [On dimension reduction in Gaussian filters](https://mlsanity.com/paper/1508.06452/) (2015)

## Built on by (most cited first, 12 of 12)

- [Computation-Aware Gaussian Processes: Model Selection And Linear-Time Inference](https://mlsanity.com/paper/2411.01036/) (2024)
- [Calibrated Computation-Aware Gaussian Processes](https://mlsanity.com/paper/2410.08796/) (2024)
- [Scalable Gaussian Processes with Latent Kronecker Structure](https://mlsanity.com/paper/2506.06895/) (2025)
- [Online Conformal Probabilistic Numerics via Adaptive Edge-Cloud Offloading](https://mlsanity.com/paper/2503.14453/) (2025)
- [Randomised Postiterations for Calibrated BayesCG](https://mlsanity.com/paper/2504.04247/) (2025)
- [Robust and Computation-Aware Gaussian Processes](https://mlsanity.com/paper/2505.21133/) (2025)
- [Bayesian Natural Gradient Fine-Tuning of CLIP Models via Kalman Filtering](https://mlsanity.com/paper/2511.01694/) (2025)
- [Gradient Regularized Natural Gradients](https://mlsanity.com/paper/2601.18420/) (2026)
- [Learning to Solve Related Linear Systems](https://mlsanity.com/paper/2503.17265/) (2025)
- [Computation-Aware Kalman Filtering with Model Selection for Neural Dynamics](https://mlsanity.com/paper/2606.01468/) (2026)
- [Modified Bryson-Frazier Smoothing and Hyperparameter Learning for Temporal Gaussian Process Regression](https://mlsanity.com/paper/2608.17595/) (2026)
- [Repairability of Inexact Solvers in Recursive State Estimation with Machine Learning](https://mlsanity.com/paper/2609.28425/) (2026)

## Abstract (arXiv)

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.