# Nonlinear Bayesian Update via Ensemble Kernel Regression with Clustering and Subsampling

arXiv: https://arxiv.org/abs/2503.15160 · HTML: https://mlsanity.com/paper/2503.15160/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 27 references that are in the map.
- First posted on arXiv 19 Mar 2025.

## Builds on (most cited first, 2 of 2)

- [Ensemble Kalman Inversion: A Derivative-Free Technique For Machine Learning Tasks](https://mlsanity.com/paper/1808.03620/) (2018)
- [Covariance inflation in the ensemble Kalman filter: a residual nudging perspective and some implications](https://mlsanity.com/paper/1305.4496/) (2013)

## Abstract (arXiv)

Nonlinear Bayesian update for a prior ensemble is proposed to extend traditional ensemble Kalman filtering to settings characterized by non-Gaussian priors and nonlinear measurement operators. In this framework, the observed component is first denoised via a standard Kalman update, while the unobserved component is estimated using a nonlinear regression approach based on kernel density estimation. The method incorporates a subsampling strategy to ensure stability and, when necessary, employs unsupervised clustering to refine the conditional estimate. Numerical experiments on Lorenz systems and a PDE-constrained inverse problem illustrate that the proposed nonlinear update can reduce estimation errors compared to standard linear updates, especially in highly nonlinear scenarios.