mlsanityData to 14 Oct 2026

Outlier-robust Kalman Filtering through Generalised Bayes

arXiv 2405.05646 ↗First posted 9 May 2024stat.ML cs.LG cs.SYcited by 21

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Abstract (arXiv)

We derive a novel, provably robust, and closed-form Bayesian update rule for online filtering in state-space models in the presence of outliers and misspecified measurement models. Our method combines generalised Bayesian inference with filtering methods such as the extended and ensemble Kalman filter. We use the former to show robustness and the latter to ensure computational efficiency in the case of nonlinear models. Our method matches or outperforms other robust filtering methods (such as those based on variational Bayes) at a much lower computational cost. We show this empirically on a range of filtering problems with outlier measurements, such as object tracking, state estimation in high-dimensional chaotic systems, and online learning of neural networks.

Key facts. Cited by 21 papers in the map (data through 14 Oct 2026). Builds on 28 of its 69 references that are in the map. First posted on arXiv 9 May 2024.

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28 of 69 references.

References · 28

  1. 2018A Tutorial on Bayesian Optimizationcited by 744
  2. 2013A General Framework for Updating Belief Distributionscited by 175
  3. 2021The Bayesian Learning Rulecited by 99
  4. 2014Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing Itcited by 95
  5. 2017Concentration of tempered posteriors and of their variational approximationscited by 66
  6. 2019Minimum Stein Discrepancy Estimatorscited by 57
  7. 2021Robust Generalised Bayesian Inference for Intractable Likelihoodscited by 53
  8. 2019Fast and Simple Natural-Gradient Variational Inference with Mixture of Exponential-family Approximationscited by 51
  9. 2018A Stein variational Newton methodcited by 50
  10. 2017Assigning a value to a power likelihood in a general Bayesian modelcited by 46
  11. 2021Martingale posterior distributionscited by 45
  12. 2015Robust Bayesian inference via coarseningcited by 32
16 more
  1. 2019Stein Point Markov Chain Monte Carlocited by 29
  2. 2020Optimal Thinning of MCMC Outputcited by 26
  3. 2017Online Natural Gradient as a Kalman Filtercited by 25
  4. 2023Low-rank extended Kalman filtering for online learning of neural networks from streaming datacited by 23
  5. 2018Doubly Robust Bayesian Inference for Non-Stationary Streaming Data with β-Divergencescited by 21
  6. 2017The Ensemble Kalman Filter: A Signal Processing Perspectivecited by 17
  7. 2023Robust and Scalable Bayesian Online Changepoint Detectioncited by 16
  8. 2021Efficient Online Bayesian Inference for Neural Banditscited by 15
  9. 2021General Bayesian Loss Function Selection and the use of Improper Modelscited by 14
  10. 2022Generalised Bayesian Inference for Discrete Intractable Likelihoodcited by 14
  11. 2023Robust and Conjugate Gaussian Process Regressioncited by 14
  12. 2023Robustifying likelihoods by optimistically re-weighting datacited by 6
  13. 2023The limited-memory recursive variational Gaussian approximation (L-RVGA)cited by 6
  14. 2023Implicit Maximum a Posteriori Filtering via Adaptive Optimizationcited by 4
  15. 2015Robust Inference for State-Space Models with Skewed Measurement Noisecited by 3
  16. 2022Robust Bayesian Inference for Moving Horizon Estimationcited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 3; 2025: 12; 2026: 6.

21 papers.

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  1. 2025On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph Learningcited by 43
  2. 2024Bayesian Online Natural Gradient (BONG)cited by 14
  3. 2025Robust and Conjugate Spatio-Temporal Gaussian Processescited by 9
  4. 2024On the Robustness of Kernel Goodness-of-Fit Testscited by 7
  5. 2024A unifying framework for generalised Bayesian online learning in non-stationary environmentscited by 5
  6. 2025Martingale Posterior Neural Networks for Fast Sequential Decision Makingcited by 4
  7. 2025Robust, Online, and Adaptive Decentralized Gaussian Processescited by 2
  8. 2025Multi-Output Robust and Conjugate Gaussian Processescited by 2
  9. 2025Bayesian Natural Gradient Fine-Tuning of CLIP Models via Kalman Filteringcited by 1
  10. 2025Robust Bayesian Optimisation with Unbounded Corruptionscited by 1
  11. 2025Tempering the Bayes Filter towards Improved Model-Based Estimationcited by 1
  12. 2026Outlier-robust Diffusion Posterior Sampling for Bayesian Inverse Problemscited by 1
9 more
  1. 2026A Predictive View on Streaming Hidden Markov Modelscited by 1
  2. 2025One Filters All: A Generalist Filter for State Estimationcited by 0
  3. 2025A theoretical framework for M-posteriors: frequentist guarantees and robustness propertiescited by 0
  4. 2025Prequential posteriorscited by 0
  5. 2025A Robust State Filter Against Unmodeled Process And Measurement Noisecited by 0
  6. 2026Active Bayesian Inference for Robust Control under Sensor False Data Injection Attackscited by 0
  7. 2026AdaKoop: Efficient Modeling of Nonlinear Dynamics from Nonstationary Data Streams with Koopman Operator Regressioncited by 0
  8. 2026Structured Noise Adaptation for Sequential Bayesian Filtering with Embedded Latent Transfer Operatorscited by 0
  9. 2026Adversarial observations in probabilistic State-Space Models for robust Reinforcement Learningcited by 0

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  2. 2025TrackDiffuser: Nearly Model-Free Bayesian Filtering with Diffusion Model
  3. 2021Uncertainty in Data-Driven Kalman Filtering for Partially Known State-Space Models
  4. 2026Neural Kalman Filtering for Unknown Dynamics: Task-Aware Learning with a Koopman Backbone ↗
  5. 2022Inverse Extended Kalman Filter -- Part I: Fundamentals
  6. 2025DnD Filter: Differentiable State Estimation for Dynamic Systems using Diffusion Models
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