# The Ensemble Kalman Update is an Empirical Matheron Update

arXiv: https://arxiv.org/abs/2502.03048 · HTML: https://mlsanity.com/paper/2502.03048/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 30 references that are in the map.
- First posted on arXiv 5 Feb 2025.

## Builds on (most cited first, 11 of 11)

- [Efficiently Sampling Functions from Gaussian Process Posteriors](https://mlsanity.com/paper/2002.09309/) (2020)
- [Mat'ern Gaussian processes on Riemannian manifolds](https://mlsanity.com/paper/2006.10160/) (2020)
- [Pathwise Conditioning of Gaussian Processes](https://mlsanity.com/paper/2011.04026/) (2020)
- [Coupling techniques for nonlinear ensemble filtering](https://mlsanity.com/paper/1907.00389/) (2019)
- [Ensemble Kalman Inversion: A Derivative-Free Technique For Machine Learning Tasks](https://mlsanity.com/paper/1808.03620/) (2018)
- [Auto-differentiable Ensemble Kalman Filters](https://mlsanity.com/paper/2107.07687/) (2021)
- [Online learning of both state and dynamics using ensemble Kalman filters](https://mlsanity.com/paper/2006.03859/) (2020)
- [Convergence Acceleration of Ensemble Kalman Inversion in Nonlinear Settings](https://mlsanity.com/paper/1911.02424/) (2019)
- [Ensemble Inference Methods for Models With Noisy and Expensive Likelihoods](https://mlsanity.com/paper/2104.03384/) (2021)
- [Gaussian Ensemble Belief Propagation for Efficient Inference in High-Dimensional Systems](https://mlsanity.com/paper/2402.08193/) (2024)
- [Ensemble Kalman Filtering for Online Gaussian Process Regression and Learning](https://mlsanity.com/paper/1807.03369/) (2018)

## Abstract (arXiv)

The Ensemble Kalman Filter (EnKF) is a widely used method for data assimilation in high-dimensional systems, with an ensemble update step equivalent to an empirical version of the Matheron update popular in Gaussian process regression -- a connection that links half a century of data-assimilation engineering to modern path-wise GP sampling. This paper provides a compact introduction to this simple but under-exploited connection, with necessary definitions accessible to all fields involved. Source code is available at https://github.com/danmackinlay/paper_matheron_equals_enkf .