# Gradient Flows in Uncertainty Propagation and Filtering of Linear Gaussian Systems

arXiv: https://arxiv.org/abs/1704.00102 · HTML: https://mlsanity.com/paper/1704.00102/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Apr 2017.

## Built on by (most cited first, 6 of 6)

- [Gradient Flows for Sampling: Mean-Field Models, Gaussian Approximations and Affine Invariance](https://mlsanity.com/paper/2302.11024/) (2023)
- [An Optimal Transport Formulation of Bayes' Law for Nonlinear Filtering Algorithms](https://mlsanity.com/paper/2203.11869/) (2022)
- [Proximal Mean Field Learning in Shallow Neural Networks](https://mlsanity.com/paper/2210.13879/) (2022)
- [Variational Gaussian approximation of the Kushner optimal filter](https://mlsanity.com/paper/2310.01859/) (2023)
- [A Distributed Algorithm for Measure-valued Optimization with Additive Objective](https://mlsanity.com/paper/2202.08930/) (2022)
- [Learning Concave Bid Shading Strategies in Online Auctions via Measure-valued Proximal Optimization](https://mlsanity.com/paper/2509.10693/) (2025)

## Abstract (arXiv)

The purpose of this work is mostly expository and aims to elucidate the Jordan-Kinderlehrer-Otto (JKO) scheme for uncertainty propagation, and a variant, the Laugesen-Mehta-Meyn-Raginsky (LMMR) scheme for filtering. We point out that these variational schemes can be understood as proximal operators in the space of density functions, realizing gradient flows. These schemes hold the promise of leading to efficient ways for solving the Fokker-Planck equation as well as the equations of non-linear filtering. Our aim in this paper is to develop in detail the underlying ideas in the setting of linear stochastic systems with Gaussian noise and recover known results.