mlsanityData to 14 Oct 2026

Finite sample properties of parametric MMD estimation: robustness to misspecification and dependence

arXiv 1912.05737 ↗First posted 12 Dec 2019math.ST cs.LG stat.COcited by 25

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Abstract (arXiv)

Many works in statistics aim at designing a universal estimation procedure, that is, an estimator that would converge to the best approximation of the (unknown) data generating distribution in a model, without any assumption on this distribution. This question is of major interest, in particular because the universality property leads to the robustness of the estimator. In this paper, we tackle the problem of universal estimation using a minimum distance estimator presented in Briol et al. (2019) based on the Maximum Mean Discrepancy. We show that the estimator is robust to both dependence and to the presence of outliers in the dataset. Finally, we provide a theoretical study of the stochastic gradient descent algorithm used to compute the estimator, and we support our findings with numerical simulations. ** The proof of Proposition 4.4 in the published version contains a mistake. The mistake is fixed here (and the bound is actually improved by a factor 2). **

Key facts. Cited by 25 papers in the map (data through 14 Oct 2026). First posted on arXiv 12 Dec 2019.

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Citing papers per year: 2021: 2; 2022: 3; 2023: 7; 2024: 4; 2025: 3; 2026: 6.

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  1. 2023Learning Robust Statistics for Simulation-based Inference under Model Misspecificationcited by 48
  2. 2022Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrapcited by 41
  3. 2021Composite Goodness-of-fit Tests with Kernelscited by 16
  4. 2023Optimally-Weighted Estimators of the Maximum Mean Discrepancy for Likelihood-Free Inferencecited by 13
  5. 2023Efficient Numerical Integration in Reproducing Kernel Hilbert Spaces via Leverage Scores Samplingcited by 10
  6. 2024Robust Kernel Hypothesis Testing under Data Corruptioncited by 7
  7. 2024On the Robustness of Kernel Goodness-of-Fit Testscited by 7
  8. 2022Variance-Aware Estimation of Kernel Mean Embeddingcited by 6
  9. 2024Data Distribution Valuationcited by 5
  10. 2021Clustering Market Regimes using the Wasserstein Distancecited by 4
  11. 2024Efficient and Accurate Explanation Estimation with Distribution Compressioncited by 4
  12. 2022Change Detection of Markov Kernels with Unknown Pre and Post Change Kernelcited by 3
13 more
  1. 2023A Semi-Bayesian Nonparametric Estimator of the Maximum Mean Discrepancy Measure: Applications in Goodness-of-Fit Testing and Generative Adversarial Networkscited by 3
  2. 2026Minimum Distance Summaries for Robust Neural Posterior Estimationcited by 3
  3. 2023Non-parametric online market regime detection and regime clustering for multidimensional and path-dependent data structurescited by 2
  4. 2025Distributional Statistics Restore Training Data Auditability in One-step Distilled Diffusion Modelscited by 2
  5. 2025Decision Making under Model Misspecification: DRO with Robust Bayesian Ambiguity Setscited by 2
  6. 2023A Bayesian Non-parametric Approach to Generative Models: Integrating Variational Autoencoder and Generative Adversarial Networks using Wasserstein and Maximum Mean Discrepancycited by 1
  7. 2026A Gradient Flow Perspective on Minimum MMD Estimationcited by 1
  8. 2023Constructing Synthetic Treatment Groups without the Mean Exchangeability Assumptioncited by 0
  9. 2025Continuous Temporal Learning of Probability Distributions via Neural ODEs with Applications in Continuous Glucose Monitoring Datacited by 0
  10. 2026Generalising maximum mean discrepancy: kernelised functional Bregman divergencescited by 0
  11. 2026Gaussian mixture models in Hilbert spaces via kernel methodscited by 0
  12. 2026Nonparametric Deconvolution and Denoising using Simulation Based Inferencecited by 0
  13. 2026Markov Chain Convergence in Kernel-Induced Geometrycited by 0