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Measuring Sample Quality with Stein's Method

arXiv 1506.03039 ↗First posted 9 Jun 2015stat.ML cs.LG math.PRcited by 94

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Abstract (arXiv)

To improve the efficiency of Monte Carlo estimation, practitioners are turning to biased Markov chain Monte Carlo procedures that trade off asymptotic exactness for computational speed. The reasoning is sound: a reduction in variance due to more rapid sampling can outweigh the bias introduced. However, the inexactness creates new challenges for sampler and parameter selection, since standard measures of sample quality like effective sample size do not account for asymptotic bias. To address these challenges, we introduce a new computable quality measure based on Stein's method that quantifies the maximum discrepancy between sample and target expectations over a large class of test functions. We use our tool to compare exact, biased, and deterministic sample sequences and illustrate applications to hyperparameter selection, convergence rate assessment, and quantifying bias-variance tradeoffs in posterior inference.

Key facts. Cited by 94 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Jun 2015.

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Citing papers per year: 2021: 22; 2022: 20; 2023: 12; 2024: 15; 2025: 11; 2026: 14.

94 papers.

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  1. 2021How to Train Your Energy-Based Modelscited by 271
  2. 2021Robust Generalised Bayesian Inference for Intractable Likelihoodscited by 53
  3. 2022Understanding DDPM Latent Codes Through Optimal Transportcited by 44
  4. 2021Generalized Kernel Thinningcited by 29
  5. 2021A Survey of Monte Carlo Methods for Parameter Estimationcited by 23
  6. 2023SteinDreamer: Variance Reduction for Text-to-3D Score Distillation via Stein Identitycited by 23
  7. 2022Gradient Estimation with Discrete Stein Operatorscited by 22
  8. 2022A Finite-Particle Convergence Rate for Stein Variational Gradient Descentcited by 22
  9. 2024Batch and match: black-box variational inference with a score-based divergencecited by 22
  10. 2022KSD Aggregated Goodness-of-fit Testcited by 21
  11. 2021Neural Variational Gradient Descentcited by 19
  12. 2023Semi-Implicit Variational Inference via Score Matchingcited by 19
38 more
  1. 2023Causal Modeling with Stationary Diffusionscited by 19
  2. 2021Variational inference with a quantum computercited by 18
  3. 2021Sampling with Mirrored Stein Operatorscited by 17
  4. 2021Composite Goodness-of-fit Tests with Kernelscited by 16
  5. 2022Targeted Separation and Convergence with Kernel Discrepanciescited by 15
  6. 2022Controlling Moments with Kernel Stein Discrepanciescited by 13
  7. 2023Entropy-based Training Methods for Scalable Neural Implicit Samplercited by 13
  8. 2024Scalable Bayesian Learning with posteriorscited by 13
  9. 2024Improved Finite-Particle Convergence Rates for Stein Variational Gradient Descentcited by 13
  10. 2021Efficient and Generalizable Tuning Strategies for Stochastic Gradient MCMCcited by 11
  11. 2022MixFlows: principled variational inference via mixed flowscited by 11
  12. 2022Scalable Bayesian Uncertainty Quantification for Neural Network Potentials: Promise and Pitfallscited by 11
  13. 2021Interpreting diffusion score matching using normalizing flowcited by 9
  14. 2021Hamiltonian Dynamics with Non-Newtonian Momentum for Rapid Samplingcited by 9
  15. 2022A kernel Stein test of goodness of fit for sequential modelscited by 9
  16. 2023Kernel Stein Discrepancy thinning: a theoretical perspective of pathologies and a practical fix with regularizationcited by 9
  17. 2023The Score-Difference Flow for Implicit Generative Modelingcited by 9
  18. 2025A Practical Introduction to Kernel Discrepancies: MMD, HSIC & KSDcited by 9
  19. 2021On Energy-Based Models with Overparametrized Shallow Neural Networkscited by 8
  20. 2022Are you using test log-likelihood correctly?cited by 8
  21. 2024Kernel Semi-Implicit Variational Inferencecited by 8
  22. 2022Posterior Coreset Construction with Kernelized Stein Discrepancy for Model-Based Reinforcement Learningcited by 7
  23. 2024On the Robustness of Kernel Goodness-of-Fit Testscited by 7
  24. 2025KerJEPA: Kernel Discrepancies for Euclidean Self-Supervised Learningcited by 6
  25. 2026Kernel-Gradient Drifting Modelscited by 6
  26. 2021Bounding Wasserstein distance with couplingscited by 5
  27. 2022Sobolev Spaces, Kernels and Discrepancies over Hyperspherescited by 5
  28. 2025Analytical Survey of Learning with Low-Resource Data: From Analysis to Investigationcited by 5
  29. 2021A Unifying and Canonical Description of Measure-Preserving Diffusionscited by 4
  30. 2021Standardisation-function Kernel Stein Discrepancy: A Unifying View on Kernel Stein Discrepancy Tests for Goodness-of-fitcited by 4
  31. 2021Geometry-informed irreversible perturbations for accelerated convergence of Langevin dynamicscited by 4
  32. 2023STEERING: Stein Information Directed Exploration for Model-Based Reinforcement Learningcited by 4
  33. 2023Using Perturbation to Improve Goodness-of-Fit Tests based on Kernelized Stein Discrepancycited by 4
  34. 2024Nystr"om Kernel Stein Discrepancycited by 4
  35. 2021Active Slices for Sliced Stein Discrepancycited by 3
  36. 2021An Easy to Interpret Diagnostic for Approximate Inference: Symmetric Divergence Over Simulationscited by 3
  37. 2021Stein Variational Gradient Descent with Multiple Kernelcited by 3
  38. 2022AgraSSt: Approximate Graph Stein Statistics for Interpretable Assessment of Implicit Graph Generatorscited by 3

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