mlsanityData to 7 Oct 2026

Stein Point Markov Chain Monte Carlo

arXiv 1905.03673 ↗First posted 9 May 2019stat.CO math.ST stat.MEcited by 29

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Abstract (arXiv)

An important task in machine learning and statistics is the approximation of a probability measure by an empirical measure supported on a discrete point set. Stein Points are a class of algorithms for this task, which proceed by sequentially minimising a Stein discrepancy between the empirical measure and the target and, hence, require the solution of a non-convex optimisation problem to obtain each new point. This paper removes the need to solve this optimisation problem by, instead, selecting each new point based on a Markov chain sample path. This significantly reduces the computational cost of Stein Points and leads to a suite of algorithms that are straightforward to implement. The new algorithms are illustrated on a set of challenging Bayesian inference problems, and rigorous theoretical guarantees of consistency are established.

Key facts. Cited by 29 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 May 2019.

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Citing papers per year: 2021: 9; 2022: 5; 2023: 5; 2024: 4; 2025: 4; 2026: 2.

29 papers.

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  1. 2021Kernel Stein Discrepancy Descentcited by 57
  2. 2021Robust Generalised Bayesian Inference for Intractable Likelihoodscited by 53
  3. 2021Kernel Thinningcited by 47
  4. 2021Generalized Kernel Thinningcited by 29
  5. 2024Outlier-robust Kalman Filtering through Generalised Bayescited by 21
  6. 2021Sampling with Mirrored Stein Operatorscited by 17
  7. 2022Targeted Separation and Convergence with Kernel Discrepanciescited by 15
  8. 2023Optimally-Weighted Estimators of the Maximum Mean Discrepancy for Likelihood-Free Inferencecited by 13
  9. 2023Kernel Stein Discrepancy thinning: a theoretical perspective of pathologies and a practical fix with regularizationcited by 9
  10. 2025Robust and Conjugate Spatio-Temporal Gaussian Processescited by 9
  11. 2025A Dictionary of Closed-Form Kernel Mean Embeddingscited by 9
  12. 2022Posterior Coreset Construction with Kernelized Stein Discrepancy for Model-Based Reinforcement Learningcited by 7
17 more
  1. 2021Performance analysis of greedy algorithms for minimising a Maximum Mean Discrepancycited by 6
  2. 2021Statistical Depth Meets Machine Learning: Kernel Mean Embeddings and Depth in Functional Data Analysiscited by 6
  3. 2023Adaptive Batch Sizes for Active Learning A Probabilistic Numerics Approachcited by 6
  4. 2022Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agentscited by 5
  5. 2021A Unifying and Canonical Description of Measure-Preserving Diffusionscited by 4
  6. 2021Standardisation-function Kernel Stein Discrepancy: A Unifying View on Kernel Stein Discrepancy Tests for Goodness-of-fitcited by 4
  7. 2023STEERING: Stein Information Directed Exploration for Model-Based Reinforcement Learningcited by 4
  8. 2024Nystr"om Kernel Stein Discrepancycited by 4
  9. 2022Online, Informative MCMC Thinning with Kernelized Stein Discrepancycited by 3
  10. 2022Proposal of a Score Based Approach to Sampling Using Monte Carlo Estimation of Score and Oracle Access to Target Densitycited by 3
  11. 2023Bayesian Numerical Integration with Neural Networkscited by 3
  12. 2026Probabilistic Inference and Learning with Stein's Methodcited by 3
  13. 2025The Minimax Lower Bound of Kernel Stein Discrepancy Estimationcited by 2
  14. 2026Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSDcited by 2
  15. 2024Monte Carlo with kernel-based Gibbs measures: Guarantees for probabilistic herdingcited by 1
  16. 2024Deterministic Fokker-Planck Transport -- With Applications to Sampling, Variational Inference, Kernel Mean Embeddings & Sequential Monte Carlocited by 0
  17. 2025Quenched large deviations for Monte Carlo integration with Coulomb gasescited by 0