mlsanityData to 7 Oct 2026

Coupling techniques for nonlinear ensemble filtering

arXiv 1907.00389 ↗First posted 30 Jun 2019stat.ME stat.CO stat.MLcited by 48

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Abstract (arXiv)

We consider filtering in high-dimensional non-Gaussian state-space models with intractable transition kernels, nonlinear and possibly chaotic dynamics, and sparse observations in space and time. We propose a novel filtering methodology that harnesses transportation of measures, convex optimization, and ideas from probabilistic graphical models to yield robust ensemble approximations of the filtering distribution in high dimensions. Our approach can be understood as the natural generalization of the ensemble Kalman filter (EnKF) to nonlinear updates, using stochastic or deterministic couplings. The use of nonlinear updates can reduce the intrinsic bias of the EnKF at a marginal increase in computational cost. We avoid any form of importance sampling and introduce non-Gaussian localization approaches for dimension scalability. Our framework achieves state-of-the-art tracking performance on challenging configurations of the Lorenz-96 model in the chaotic regime.

Key facts. Cited by 48 papers in the map (data through 7 Oct 2026). First posted on arXiv 30 Jun 2019.

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Citing papers per year: 2021: 5; 2022: 6; 2023: 11; 2024: 9; 2025: 7; 2026: 10.

48 papers.

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  1. 2022Conditional Simulation Using Diffusion Schr"odinger Bridgescited by 58
  2. 2023An Ensemble Score Filter for Tracking High-Dimensional Nonlinear Dynamical Systemscited by 33
  3. 2024Sampling in Unit Time with Kernel Fisher-Rao Flowcited by 27
  4. 2023Conditional Optimal Transport on Function Spacescited by 26
  5. 2024Dynamic Conditional Optimal Transport through Simulation-Free Flowscited by 24
  6. 2023Efficient Neural Network Approaches for Conditional Optimal Transport with Applications in Bayesian Inferencecited by 19
  7. 2022On minimax density estimation via measure transportcited by 18
  8. 2021Learning non-Gaussian graphical models via Hessian scores and triangular transportcited by 16
  9. 2022An Optimal Transport Formulation of Bayes' Law for Nonlinear Filtering Algorithmscited by 11
  10. 2025Learning Enhanced Ensemble Filterscited by 11
  11. 2025Flow Matching for Efficient and Scalable Data Assimilationcited by 11
  12. 2023Nonlinear Filtering with Brenier Optimal Transport Mapscited by 10
36 more
  1. 2021Scalable conditional deep inverse Rosenblatt transports using tensor-trains and gradient-based dimension reductioncited by 9
  2. 2022Ensemble transport smoothing. Part II: Nonlinear updatescited by 8
  3. 2023A generative flow for conditional sampling via optimal transportcited by 7
  4. 2024Learning Optimal Filters Using Variational Inferencecited by 7
  5. 2024Nonlinear Assimilation via Score-based Sequential Langevin Samplingcited by 7
  6. 2022A low-rank ensemble Kalman filter for elliptic observationscited by 6
  7. 2022Ensemble transport smoothing. Part I: Unified frameworkcited by 5
  8. 2024BI-EqNO: Generalized Approximate Bayesian Inference with an Equivariant Neural Operator Frameworkcited by 5
  9. 2023Exact nonlinear state estimationcited by 4
  10. 2025Fast filtering of non-Gaussian models using Amortized Optimal Transport Mapscited by 4
  11. 2025A friendly introduction to triangular transportcited by 4
  12. 2025Flow-based Bayesian filtering for high-dimensional nonlinear stochastic dynamical systemscited by 3
  13. 2026Latent Autoencoder Ensemble Kalman Filter for Nonlinear Data assimilationcited by 3
  14. 2026Closed-form conditional diffusion models for data assimilationcited by 3
  15. 2021Machine learning-based conditional mean filter: a generalization of the ensemble Kalman filter for nonlinear data assimilationcited by 2
  16. 2023A transport approach to sequential simulation-based inferencecited by 2
  17. 2023Density Estimation via Measure Transport: Outlook for Applications in the Biological Sciencescited by 2
  18. 2024Ensemble Transport Filter via Optimized Maximum Mean Discrepancycited by 2
  19. 2024Recurrent Interpolants for Probabilistic Time Series Predictioncited by 2
  20. 2025Efficient Transformed Gaussian Process State-Space Models for Non-Stationary High-Dimensional Dynamical Systemscited by 2
  21. 2026Amortized Filtering and Smoothing with Conditional Normalizing Flowscited by 2
  22. 2021Incremental Non-Gaussian Inference for SLAM Using Normalizing Flowscited by 1
  23. 2023Progressive Bayesian Particle Flows based on Optimal Transport Map Sequencescited by 1
  24. 2023Leveraging joint sparsity in hierarchical Bayesian learningcited by 1
  25. 2023An adaptive ensemble filter for heavy-tailed distributions: tuning-free inflation and localizationcited by 1
  26. 2024Sequential transport maps using SoS density estimation and α-divergencescited by 1
  27. 2026Pathwise Learning of Stochastic Dynamical Systems with Partial Observationscited by 1
  28. 2026Adaptive Nonlinear Data Assimilation through P-Spline Triangular Measure Transportcited by 1
  29. 2021Affine-Mapping based Variational Ensemble Kalman Filtercited by 0
  30. 2024Preserving linear invariants in ensemble filtering methodscited by 0
  31. 2025The Ensemble Kalman Update is an Empirical Matheron Updatecited by 0
  32. 2026Conditional Normalizing Flows for Forward and Backward Joint State and Parameter Estimationcited by 0
  33. 2026Coupling-Informed Transport Maps for Bayesian Filtering in Nonlinear Dynamical Systemscited by 0
  34. 2026Generative models for simulation based filtering: Formulations and Empirical Comparisonscited by 0
  35. 2026One-Step Generative Surrogate Models via Block-Triangular Joint Driftingcited by 0
  36. 2026Learning the Structure of Triangular Transport Mapscited by 0