mlsanityData to 7 Oct 2026

Control functionals for Monte Carlo integration

arXiv 1410.2392 ↗First posted 9 Oct 2014stat.MEcited by 59

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Abstract (arXiv)

A non-parametric extension of control variates is presented. These leverage gradient information on the sampling density to achieve substantial variance reduction. It is not required that the sampling density be normalised. The novel contribution of this work is based on two important insights; (i) a trade-off between random sampling and deterministic approximation and (ii) a new gradient-based function space derived from Stein's identity. Unlike classical control variates, our estimators achieve super-root-n convergence, often requiring orders of magnitude fewer simulations to achieve a fixed level of precision. Theoretical and empirical results are presented, the latter focusing on integration problems arising in hierarchical models and models based on non-linear ordinary differential equations.

Key facts. Cited by 59 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Oct 2014.

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Citing papers per year: 2021: 9; 2022: 8; 2023: 7; 2024: 11; 2025: 9; 2026: 15.

59 papers.

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  1. 2021Kernel Thinningcited by 47
  2. 2024Distillation of Discrete Diffusion through Dimensional Correlationscited by 46
  3. 2021Generalized Kernel Thinningcited by 29
  4. 2021Positively Weighted Kernel Quadrature via Subsamplingcited by 25
  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. 2022Fast Bayesian Inference with Batch Bayesian Quadrature via Kernel Recombinationcited by 20
  9. 2021Sampling with Mirrored Stein Operatorscited by 17
  10. 2021Composite Goodness-of-fit Tests with Kernelscited by 16
  11. 2022Targeted Separation and Convergence with Kernel Discrepanciescited by 15
  12. 2022Controlling Moments with Kernel Stein Discrepanciescited by 13
38 more
  1. 2024Stein transport for Bayesian inferencecited by 11
  2. 2022A kernel Stein test of goodness of fit for sequential modelscited by 9
  3. 2023Stabilizing Estimates of Shapley Values with Control Variatescited by 9
  4. 2025A Dictionary of Closed-Form Kernel Mean Embeddingscited by 9
  5. 2024Sliced-Wasserstein Estimation with Spherical Harmonics as Control Variatescited by 8
  6. 2024On the Robustness of Kernel Goodness-of-Fit Testscited by 7
  7. 2026Reverse Flow Matching: A Unified Framework for Online Reinforcement Learning with Diffusion and Flow Policiescited by 7
  8. 2021Performance analysis of greedy algorithms for minimising a Maximum Mean Discrepancycited by 6
  9. 2023Meta-learning Control Variates: Variance Reduction with Limited Datacited by 6
  10. 2022Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agentscited by 5
  11. 2025Nested Expectations with Kernel Quadraturecited by 5
  12. 2025Distribution estimation via Flow Matching with Lipschitz guaranteescited by 5
  13. 2021Gaussian Processes on Hypergraphscited by 4
  14. 2022Variance Reduction for Policy-Gradient Methods via Empirical Variance Minimizationcited by 4
  15. 2023Theoretical guarantees for neural control variates in MCMCcited by 4
  16. 2023When can Regression-Adjusted Control Variates Help? Rare Events, Sobolev Embedding and Minimax Optimalitycited by 4
  17. 2024Nystr"om Kernel Stein Discrepancycited by 4
  18. 2023Bayesian Numerical Integration with Neural Networkscited by 3
  19. 2024A Quadrature Approach for General-Purpose Batch Bayesian Optimization via Probabilistic Liftingcited by 3
  20. 2026Probabilistic Inference and Learning with Stein's Methodcited by 3
  21. 2026Aligning Few-Step Generative Models by Amortizing Sample-based Variational Inferencecited by 3
  22. 2022A Quadrature Rule combining Control Variates and Adaptive Importance Samplingcited by 2
  23. 2024Kernelized Normalizing Constant Estimation: Bridging Bayesian Quadrature and Bayesian Optimizationcited by 2
  24. 2024Prediction-Enhanced Monte Carlo: A Machine Learning View on Control Variatecited by 2
  25. 2025Stationary MMD Pointscited by 2
  26. 2025The Minimax Lower Bound of Kernel Stein Discrepancy Estimationcited by 2
  27. 2026Conditional neural control variates for variance reduction in Bayesian inverse problemscited by 2
  28. 2026Kernel Tests of Equivalencecited by 2
  29. 2026Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSDcited by 2
  30. 2021Tractable Computation of Expected Kernelscited by 1
  31. 2024Monte Carlo with kernel-based Gibbs measures: Guarantees for probabilistic herdingcited by 1
  32. 2026Learning Policy Representations for Steerable Behavior Synthesiscited by 1
  33. 2026Bayesian Quadraturecited by 1
  34. 2023Empirical Bayes Estimation with Side Information: A Nonparametric Integrative Tweedie Approachcited by 0
  35. 2024Feynman-Kac Operator Expectation Estimatorcited by 0
  36. 2024Pathwise Gradient Variance Reduction with Control Variates in Variational Inferencecited by 0
  37. 2025Minimax Optimal Two-Stage Algorithm For Moment Estimation Under Covariate Shiftcited by 0
  38. 2025Copula Discrepancy: Benchmarking Dependence Structurecited by 0

50 most cited of 59 All 59 (JSON)