mlsanityData to 7 Oct 2026

Minimum Stein Discrepancy Estimators

arXiv 1906.08283 ↗First posted 19 Jun 2019math.ST cs.LG stat.MEcited by 57

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Abstract (arXiv)

When maximum likelihood estimation is infeasible, one often turns to score matching, contrastive divergence, or minimum probability flow to obtain tractable parameter estimates. We provide a unifying perspective of these techniques as minimum Stein discrepancy estimators, and use this lens to design new diffusion kernel Stein discrepancy (DKSD) and diffusion score matching (DSM) estimators with complementary strengths. We establish the consistency, asymptotic normality, and robustness of DKSD and DSM estimators, then derive stochastic Riemannian gradient descent algorithms for their efficient optimisation. The main strength of our methodology is its flexibility, which allows us to design estimators with desirable properties for specific models at hand by carefully selecting a Stein discrepancy. We illustrate this advantage for several challenging problems for score matching, such as non-smooth, heavy-tailed or light-tailed densities.

Key facts. Cited by 57 papers in the map (data through 7 Oct 2026). First posted on arXiv 19 Jun 2019.

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Citing papers per year: 2021: 11; 2022: 13; 2023: 10; 2024: 6; 2025: 10; 2026: 7.

57 papers.

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  1. 2022Score matching enables causal discovery of nonlinear additive noise modelscited by 108
  2. 2022Statistical Efficiency of Score Matching: The View from Isoperimetrycited by 63
  3. 2024Informed Correctors for Discrete Diffusion Modelscited by 57
  4. 2021Robust Generalised Bayesian Inference for Intractable Likelihoodscited by 53
  5. 2022Gradient Estimation with Discrete Stein Operatorscited by 22
  6. 2024Batch and match: black-box variational inference with a score-based divergencecited by 22
  7. 2022KSD Aggregated Goodness-of-fit Testcited by 21
  8. 2024Outlier-robust Kalman Filtering through Generalised Bayescited by 21
  9. 2023Provable benefits of score matchingcited by 18
  10. 2021Sampling with Mirrored Stein Operatorscited by 17
  11. 2021Composite Goodness-of-fit Tests with Kernelscited by 16
  12. 2023Robust and Scalable Bayesian Online Changepoint Detectioncited by 16
38 more
  1. 2022Targeted Separation and Convergence with Kernel Discrepanciescited by 15
  2. 2022Generalised Bayesian Inference for Discrete Intractable Likelihoodcited by 14
  3. 2023Robust and Conjugate Gaussian Process Regressioncited by 14
  4. 2022Towards Healing the Blindness of Score Matchingcited by 13
  5. 2022Controlling Moments with Kernel Stein Discrepanciescited by 13
  6. 2021A Computationally Efficient Method for Learning Exponential Family Distributionscited by 10
  7. 2023Sampling Multimodal Distributions with the Vanilla Score: Benefits of Data-Based Initializationcited by 10
  8. 2023Particle-based Variational Inference with Generalized Wasserstein Gradient Flowcited by 10
  9. 2021Interpreting diffusion score matching using normalizing flowcited by 9
  10. 2022A kernel Stein test of goodness of fit for sequential modelscited by 9
  11. 2023Energy Discrepancies: A Score-Independent Loss for Energy-Based Modelscited by 9
  12. 2025Robust and Conjugate Spatio-Temporal Gaussian Processescited by 9
  13. 2025A Dictionary of Closed-Form Kernel Mean Embeddingscited by 9
  14. 2021On Energy-Based Models with Overparametrized Shallow Neural Networkscited by 8
  15. 2024On the Robustness of Kernel Goodness-of-Fit Testscited by 7
  16. 2023Fit Like You Sample: Sample-Efficient Generalized Score Matching from Fast Mixing Diffusionscited by 6
  17. 2022Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agentscited by 5
  18. 2021A Unifying and Canonical Description of Measure-Preserving Diffusionscited by 4
  19. 2021Standardisation-function Kernel Stein Discrepancy: A Unifying View on Kernel Stein Discrepancy Tests for Goodness-of-fitcited by 4
  20. 2024Inclusive KL Gradient Flows: Otto-Wasserstein, Fisher-Rao-Gaussian, and Local-Estimator Dynamicscited by 4
  21. 2021De-randomizing MCMC dynamics with the diffusion Stein operatorcited by 3
  22. 2022AgraSSt: Approximate Graph Stein Statistics for Interpretable Assessment of Implicit Graph Generatorscited by 3
  23. 2023Bayesian Numerical Integration with Neural Networkscited by 3
  24. 2024Data-centric Prediction Explanation via Kernelized Stein Discrepancycited by 3
  25. 2026Probabilistic Inference and Learning with Stein's Methodcited by 3
  26. 2026Minimax Estimation of Kernel Stein Discrepancy: Trace versus Hilbert-Schmidt Scalescited by 3
  27. 2021A Stein Goodness of fit Test for Exponential Random Graph Modelscited by 2
  28. 2022Neural Stein critics with staged L2-regularizationcited by 2
  29. 2023On Computationally Efficient Learning of Exponential Family Distributionscited by 2
  30. 2025Low Stein Discrepancy via Message-Passing Monte Carlocited by 2
  31. 2025Diffusion-Based Hypothesis Testing and Change-Point Detectioncited by 2
  32. 2026Efficient Learning of Stationary Diffusions with Stein-type Discrepanciescited by 2
  33. 2021Separation Results between Fixed-Kernel and Feature-Learning Probability Metricscited by 1
  34. 2022A Kernelised Stein Statistic for Assessing Implicit Generative Modelscited by 1
  35. 2023Approximate Stein Classes for Truncated Density Estimationcited by 1
  36. 2025Towards Identifiability of Interventional Stochastic Differential Equationscited by 1
  37. 2025Multi-Output Robust and Conjugate Gaussian Processescited by 1
  38. 2025Optimizing Kernel Discrepancies via Subset Selectioncited by 1

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