mlsanityData to 7 Oct 2026

Optimally-Weighted Estimators of the Maximum Mean Discrepancy for Likelihood-Free Inference

arXiv 2301.11674 ↗First posted 27 Jan 2023stat.ME stat.CO stat.MLcited by 13

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Abstract (arXiv)

Likelihood-free inference methods typically make use of a distance between simulated and real data. A common example is the maximum mean discrepancy (MMD), which has previously been used for approximate Bayesian computation, minimum distance estimation, generalised Bayesian inference, and within the nonparametric learning framework. The MMD is commonly estimated at a root-m rate, where m is the number of simulated samples. This can lead to significant computational challenges since a large m is required to obtain an accurate estimate, which is crucial for parameter estimation. In this paper, we propose a novel estimator for the MMD with significantly improved sample complexity. The estimator is particularly well suited for computationally expensive smooth simulators with low- to mid-dimensional inputs. This claim is supported through both theoretical results and an extensive simulation study on benchmark simulators.

Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Builds on 37 of its 100 references that are in the map. First posted on arXiv 27 Jan 2023.

Builds on

37 of 100 references.

References · 37

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  3. 2016Kernel Mean Embedding of Distributions: A Review and Beyondcited by 360
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  8. 2021Benchmarking Simulation-Based Inferencecited by 160
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  10. 2015Bayesian Optimization for Likelihood-Free Inference of Simulator-Based Statistical Modelscited by 61
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25 more
  1. 2019Statistical Inference for Generative Models with Maximum Mean Discrepancycited by 43
  2. 2022Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrapcited by 41
  3. 2016Support pointscited by 39
  4. 2019MMD-Bayes: Robust Bayesian Estimation via Maximum Mean Discrepancycited by 35
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  7. 2021Sequential Neural Posterior and Likelihood Approximationcited by 30
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  12. 2020Optimal Thinning of MCMC Outputcited by 25
  13. 2019Finite sample properties of parametric MMD estimation: robustness to misspecification and dependencecited by 24
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  15. 2017Convergence Analysis of Deterministic Kernel-Based Quadrature Rules in Misspecified Settingscited by 16
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 4; 2025: 6; 2026: 1.

13 papers.

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  1. 2023Learning Robust Statistics for Simulation-based Inference under Model Misspecificationcited by 48
  2. 2024A Practical Guide to Sample-based Statistical Distances for Evaluating Generative Models in Sciencecited by 14
  3. 2024FOOGD: Federated Collaboration for Both Out-of-distribution Generalization and Detectioncited by 14
  4. 2025A Dictionary of Closed-Form Kernel Mean Embeddingscited by 9
  5. 2024Conditional Bayesian Quadraturecited by 8
  6. 2024Cost-aware simulation-based inferencecited by 6
  7. 2025Nested Expectations with Kernel Quadraturecited by 5
  8. 2025Multilevel neural simulation-based inferencecited by 5
  9. 2023A Semi-Bayesian Nonparametric Estimator of the Maximum Mean Discrepancy Measure: Applications in Goodness-of-Fit Testing and Generative Adversarial Networkscited by 3
  10. 2025Representative, Informative, and De-Amplifying: Requirements for Robust Bayesian Active Learning under Model Misspecificationcited by 1
  11. 2025Kernel Quantile Embeddings and Associated Probability Metricscited by 0
  12. 2025BayesSum: Bayesian Quadrature in Discrete Spacescited by 0
1 more
  1. 2026A Gradient Flow Perspective on Minimum MMD Estimationcited by 0