mlsanityData to 7 Oct 2026

MMD-Bayes: Robust Bayesian Estimation via Maximum Mean Discrepancy

arXiv 1909.13339 ↗First posted 29 Sep 2019math.ST cs.LG stat.MLcited by 35

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Abstract (arXiv)

In some misspecified settings, the posterior distribution in Bayesian statistics may lead to inconsistent estimates. To fix this issue, it has been suggested to replace the likelihood by a pseudo-likelihood, that is the exponential of a loss function enjoying suitable robustness properties. In this paper, we build a pseudo-likelihood based on the Maximum Mean Discrepancy, defined via an embedding of probability distributions into a reproducing kernel Hilbert space. We show that this MMD-Bayes posterior is consistent and robust to model misspecification. As the posterior obtained in this way might be intractable, we also prove that reasonable variational approximations of this posterior enjoy the same properties. We provide details on a stochastic gradient algorithm to compute these variational approximations. Numerical simulations indeed suggest that our estimator is more robust to misspecification than the ones based on the likelihood.

Key facts. Cited by 35 papers in the map (data through 7 Oct 2026). First posted on arXiv 29 Sep 2019.

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Citing papers per year: 2021: 3; 2022: 7; 2023: 11; 2024: 5; 2025: 7; 2026: 2.

35 papers.

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  1. 2021Robust Generalised Bayesian Inference for Intractable Likelihoodscited by 53
  2. 2023Learning Robust Statistics for Simulation-based Inference under Model Misspecificationcited by 48
  3. 2022Robust Neural Posterior Estimation and Statistical Model Criticismcited by 45
  4. 2022Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrapcited by 41
  5. 2021Probabilistic Forecasting with Generative Networks via Scoring Rule Minimizationcited by 35
  6. 2024Addressing Misspecification in Simulation-based Inference through Data-driven Calibrationcited by 26
  7. 2023Generalized Bayesian Inference for Scientific Simulators via Amortized Cost Estimationcited by 17
  8. 2021Composite Goodness-of-fit Tests with Kernelscited by 16
  9. 2023Robust and Scalable Bayesian Online Changepoint Detectioncited by 16
  10. 2022Targeted Separation and Convergence with Kernel Discrepanciescited by 15
  11. 2022Likelihood-Free Inference with Generative Neural Networks via Scoring Rule Minimizationcited by 14
  12. 2022Generalised Bayesian Inference for Discrete Intractable Likelihoodcited by 14
23 more
  1. 2023Robust and Conjugate Gaussian Process Regressioncited by 14
  2. 2023Optimally-Weighted Estimators of the Maximum Mean Discrepancy for Likelihood-Free Inferencecited by 13
  3. 2025Integral Imprecise Probability Metricscited by 11
  4. 2022Robust Bayesian Learning for Reliable Wireless AI: Framework and Applicationscited by 9
  5. 2025Simulation-based Bayesian inference under model misspecificationcited by 9
  6. 2025A Dictionary of Closed-Form Kernel Mean Embeddingscited by 9
  7. 2023Misspecification-robust Sequential Neural Likelihood for Simulation-based Inferencecited by 8
  8. 2024Robust Kernel Hypothesis Testing under Data Corruptioncited by 7
  9. 2024On the Robustness of Kernel Goodness-of-Fit Testscited by 7
  10. 2022Robust PACm: Training Ensemble Models Under Misspecification and Outlierscited by 6
  11. 2023Deceptive Fairness Attacks on Graphs via Meta Learningcited by 6
  12. 2024Continual learning with the neural tangent ensemblecited by 4
  13. 2023A Semi-Bayesian Nonparametric Estimator of the Maximum Mean Discrepancy Measure: Applications in Goodness-of-Fit Testing and Generative Adversarial Networkscited by 3
  14. 2024A Primer on Variational Inference for Physics-Informed Deep Generative Modellingcited by 3
  15. 2025Signature Maximum Mean Discrepancy Two-Sample Statistical Testscited by 3
  16. 2026Minimum Distance Summaries for Robust Neural Posterior Estimationcited by 3
  17. 2023Some challenges of calibrating differentiable agent-based modelscited by 2
  18. 2025Decision Making under Model Misspecification: DRO with Robust Bayesian Ambiguity Setscited by 2
  19. 2023Bayes Hilbert Spaces for Posterior Approximationcited by 1
  20. 2025Inferring Optical Tissue Properties from Photoplethysmography using Hybrid Amortized Inferencecited by 1
  21. 2023Pseudo-Likelihood Inferencecited by 0
  22. 2025Kernel Quantile Embeddings and Associated Probability Metricscited by 0
  23. 2026A Gradient Flow Perspective on Minimum MMD Estimationcited by 0