mlsanityData to 7 Oct 2026

Ensemble Kalman Inversion: A Derivative-Free Technique For Machine Learning Tasks

arXiv 1808.03620 ↗First posted 10 Aug 2018cs.LG math.OC stat.MLcited by 36

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Abstract (arXiv)

The standard probabilistic perspective on machine learning gives rise to empirical risk-minimization tasks that are frequently solved by stochastic gradient descent (SGD) and variants thereof. We present a formulation of these tasks as classical inverse or filtering problems and, furthermore, we propose an efficient, gradient-free algorithm for finding a solution to these problems using ensemble Kalman inversion (EKI). Applications of our approach include offline and online supervised learning with deep neural networks, as well as graph-based semi-supervised learning. The essence of the EKI procedure is an ensemble based approximate gradient descent in which derivatives are replaced by differences from within the ensemble. We suggest several modifications to the basic method, derived from empirically successful heuristics developed in the context of SGD. Numerical results demonstrate wide applicability and robustness of the proposed algorithm.

Key facts. Cited by 36 papers in the map (data through 7 Oct 2026). First posted on arXiv 10 Aug 2018.

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Citing papers per year: 2021: 4; 2022: 4; 2023: 9; 2024: 7; 2025: 9; 2026: 3.

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  1. 2025InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciencescited by 67
  2. 2024Ensemble Kalman Diffusion Guidance: A Derivative-free Method for Inverse Problemscited by 18
  3. 2021Towards physically consistent data-driven weather forecasting: Integrating data assimilation with equivariance-preserving deep spatial transformerscited by 15
  4. 2021Bridging observation, theory and numerical simulation of the ocean using Machine Learningcited by 15
  5. 2023Neural Dynamical Operator: Continuous Spatial-Temporal Model with Gradient-Based and Derivative-Free Optimization Methodscited by 14
  6. 2021Scaling Up Bayesian Uncertainty Quantification for Inverse Problems using Deep Neural Networkscited by 9
  7. 2023Gradient-free training of neural ODEs for system identification and control using ensemble Kalman inversioncited by 9
  8. 2021Ensemble Inference Methods for Models With Noisy and Expensive Likelihoodscited by 8
  9. 2022Non-Asymptotic Analysis of Ensemble Kalman Updates: Effective Dimension and Localizationcited by 7
  10. 2024Hyperparameter Optimization for Randomized Algorithms: A Case Study on Random Featurescited by 7
  11. 2022Second Order Ensemble Langevin Method for Sampling and Inverse Problemscited by 6
  12. 2023Efficient Bayesian Physics Informed Neural Networks for Inverse Problems via Ensemble Kalman Inversioncited by 6
24 more
  1. 2023Gradient-free online learning of subgrid-scale dynamics with neural emulatorscited by 5
  2. 2025Active Learning of Model Discrepancy with Bayesian Experimental Designcited by 5
  3. 2023Online Calibration of Deep Learning Sub-Models for Hybrid Numerical Modeling Systemscited by 4
  4. 2024Uncertainty quantification for deeponets with ensemble kalman inversioncited by 4
  5. 2025Blade: A Derivative-free Bayesian Inversion Method using Diffusion Priorscited by 3
  6. 2023Flow Annealed Kalman Inversion for Gradient-Free Inference in Bayesian Inverse Problemscited by 2
  7. 2023Extreme Event Prediction with Multi-agent Reinforcement Learning-based Parametrization of Atmospheric and Oceanic Turbulencecited by 2
  8. 2024Derivative-Free Diffusion Manifold-Constrained Gradient for Unified XAIcited by 2
  9. 2025Scalable Bayesian Physics-Informed Kolmogorov-Arnold Networkscited by 2
  10. 2025Bayesian Experimental Design for Model Discrepancy Calibration: An Auto-Differentiable Ensemble Kalman Inversion Approachcited by 2
  11. 2022A unified method of data assimilation and turbulence modeling for separated flows at high Reynolds numberscited by 1
  12. 2024Private Knowledge Sharing in Distributed Learning: A Surveycited by 1
  13. 2024Adjoint-based online learning of two-layer quasi-geostrophic baroclinic turbulencecited by 1
  14. 2025Nesterov Acceleration for Ensemble Kalman Inversion and Variantscited by 1
  15. 2022Variational Kalman Filtering with Hinf-Based Correction for Robust Bayesian Learning in High Dimensionscited by 0
  16. 2023Reweighted Interacting Langevin Diffusions: an Accelerated Sampling Methodfor Optimizationcited by 0
  17. 2023Affine Invariant Ensemble Transform Methods to Improve Predictive Uncertainty in Neural Networkscited by 0
  18. 2024Training neural networks without backpropagation using particlescited by 0
  19. 2025The Ensemble Kalman Update is an Empirical Matheron Updatecited by 0
  20. 2025Nonlinear Bayesian Update via Ensemble Kernel Regression with Clustering and Subsamplingcited by 0
  21. 2025Ensemble Kalman filter for uncertainty in human language comprehensioncited by 0
  22. 2026Bayesian Experimental Design for Model Discrepancy Calibration: A Rivalry between Kullback--Leibler Divergence and Wasserstein Distancecited by 0
  23. 2026Active Learning for Communication Structure Optimization in LLM-Based Multi-Agent Systemscited by 0
  24. 2026Functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networkscited by 0