mlsanityData to 14 Oct 2026

Low Stein Discrepancy via Message-Passing Monte Carlo

arXiv 2503.21103 ↗First posted 27 Mar 2025cs.LG cs.NA math.NAcited by 2

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Abstract (arXiv)

Message-Passing Monte Carlo (MPMC) was recently introduced as a novel low-discrepancy sampling approach leveraging tools from geometric deep learning. While originally designed for generating uniform point sets, we extend this framework to sample from general multivariate probability distributions with known probability density function. Our proposed method, Stein-Message-Passing Monte Carlo (Stein-MPMC), minimizes a kernelized Stein discrepancy, ensuring improved sample quality. Finally, we show that Stein-MPMC outperforms competing methods, such as Stein Variational Gradient Descent and (greedy) Stein Points, by achieving a lower Stein discrepancy.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 15 of its 28 references that are in the map. First posted on arXiv 27 Mar 2025.

Builds on

15 of 28 references.

References · 15

  1. 2018Neural Ordinary Differential Equationscited by 3,779
  2. 2019Optuna: A Next-generation Hyperparameter Optimization Frameworkcited by 2,501
  3. 2015Variational Inference with Normalizing Flowscited by 2,170
  4. 2016Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithmcited by 507
  5. 2016A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluationcited by 236
  6. 2017Stein Variational Gradient Descent as Gradient Flowcited by 152
  7. 2016A Kernel Test of Goodness of Fitcited by 143
  8. 2017Measuring Sample Quality with Kernelscited by 119
  9. 2015Measuring Sample Quality with Stein's Methodcited by 94
  10. 2019Minimum Stein Discrepancy Estimatorscited by 57
  11. 2018Stein Pointscited by 43
  12. 2020Stochastic Stein Discrepanciescited by 30
3 more
  1. 2018Stein Variational Gradient Descent Without Gradientcited by 12
  2. 2024Message-Passing Monte Carlo: Generating low-discrepancy point sets via Graph Neural Networkscited by 6
  3. 2024Improving Efficiency of Sampling-based Motion Planning via Message-Passing Monte Carlocited by 5

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Cited by year

Citing papers per year: 2025: 2.

2 papers.

  1. 2025Neural Low-Discrepancy Sequencescited by 1
  2. 2025Learning Geometric-Aware Quadrature Rules for Functional Minimizationcited by 0