mlsanityData to 7 Oct 2026

An Optimal Transport Formulation of Bayes' Law for Nonlinear Filtering Algorithms

arXiv 2203.11869 ↗First posted 22 Mar 2022math.OC cs.SY eess.SYcited by 11

Not on the map. Why?

Abstract (arXiv)

This paper presents a variational representation of the Bayes' law using optimal transportation theory. The variational representation is in terms of the optimal transportation between the joint distribution of the (state, observation) and their independent coupling. By imposing certain structure on the transport map, the solution to the variational problem is used to construct a Brenier-type map that transports the prior distribution to the posterior distribution for any value of the observation signal. The new formulation is used to derive the optimal transport form of the Ensemble Kalman filter (EnKF) for the discrete-time filtering problem and propose a novel extension of EnKF to the non-Gaussian setting utilizing input convex neural networks. Finally, the proposed methodology is used to derive the optimal transport form of the feedback particle filler (FPF) in the continuous-time limit, which constitutes its first variational construction without explicitly using the nonlinear filtering equation or Bayes' law.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). Builds on 15 of its 41 references that are in the map. First posted on arXiv 22 Mar 2022.

Builds on

15 of 41 references.

References · 15

  1. 2018Computational Optimal Transportcited by 765
  2. 2016Input Convex Neural Networkscited by 407
  3. 2019Optimal transport mapping via input convex neural networkscited by 202
  4. 2018Optimal Control Via Neural Networks: A Convex Approachcited by 82
  5. 2022Conditional Simulation Using Diffusion Schr"odinger Bridgescited by 58
  6. 2019Coupling techniques for nonlinear ensemble filteringcited by 48
  7. 2021Preconditioned training of normalizing flows for variational inference in inverse problemscited by 19
  8. 2016An introduction to sampling via measure transportcited by 16
  9. 2022The efficacy and generalizability of conditional GANs for posterior inference in physics-based inverse problemscited by 15
  10. 2017Gradient Flows in Filtering and Fisher-Rao Geometrycited by 12
  11. 2014Poisson's equation in nonlinear filteringcited by 10
  12. 2017Gradient Flows in Uncertainty Propagation and Filtering of Linear Gaussian Systemscited by 6
3 more
  1. 2021Optimal Transportation Methods in Nonlinear Filtering: The feedback particle filtercited by 5
  2. 2019Proximal Recursion for the Wonham Filtercited by 4
  3. 2019An Optimal Transport Formulation of the Ensemble Kalman Filtercited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 4; 2024: 1; 2025: 1; 2026: 4.

11 papers.

  1. 2024Sampling in Unit Time with Kernel Fisher-Rao Flowcited by 27
  2. 2023Conditional Optimal Transport on Function Spacescited by 26
  3. 2022Reliable amortized variational inference with physics-based latent distribution correctioncited by 25
  4. 2023Nonlinear Filtering with Brenier Optimal Transport Mapscited by 10
  5. 2023A generative flow for conditional sampling via optimal transportcited by 7
  6. 2023Exact nonlinear state estimationcited by 4
  7. 2025Fast filtering of non-Gaussian models using Amortized Optimal Transport Mapscited by 4
  8. 2026Closed-form conditional diffusion models for data assimilationcited by 3
  9. 2026Energy-based Transport for Amortized Bayesian Inferencecited by 0
  10. 2026A lift for input-convex neural net trainingcited by 0
  11. 2026Generative models for simulation based filtering: Formulations and Empirical Comparisonscited by 0