# Affine-Mapping based Variational Ensemble Kalman Filter

arXiv: https://arxiv.org/abs/2103.06315 · HTML: https://mlsanity.com/paper/2103.06315/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 44 references that are in the map.
- First posted on arXiv 10 Mar 2021.

## Builds on (most cited first, 4 of 4)

- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Coupling techniques for nonlinear ensemble filtering](https://mlsanity.com/paper/1907.00389/) (2019)
- [Deterministic Mean-field Ensemble Kalman Filtering](https://mlsanity.com/paper/1409.0628/) (2014)
- [Trimmed Ensemble Kalman Filter for Nonlinear and Non-Gaussian Data Assimilation Problems](https://mlsanity.com/paper/1808.05465/) (2018)

## Abstract (arXiv)

We propose an affine-mapping based variational Ensemble Kalman filter for sequential Bayesian filtering problems with generic observation models. Specifically, the proposed method is formulated as to construct an affine mapping from the prior ensemble to the posterior one, and the affine mapping is computed via a variational Bayesian formulation, i.e., by minimizing the Kullback-Leibler divergence between the transformed distribution through the affine mapping and the actual posterior. Some theoretical properties of resulting optimization problem are studied and a gradient descent scheme is proposed to solve the resulting optimization problem. With numerical examples we demonstrate that the method has competitive performance against existing methods.