# Low Stein Discrepancy via Message-Passing Monte Carlo

arXiv: https://arxiv.org/abs/2503.21103 · HTML: https://mlsanity.com/paper/2503.21103/

## 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 (most cited first, 15 of 15)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [Stein Variational Gradient Descent as Gradient Flow](https://mlsanity.com/paper/1704.07520/) (2017)
- [A Kernel Test of Goodness of Fit](https://mlsanity.com/paper/1602.02964/) (2016)
- [Measuring Sample Quality with Kernels](https://mlsanity.com/paper/1703.01717/) (2017)
- [Measuring Sample Quality with Stein's Method](https://mlsanity.com/paper/1506.03039/) (2015)
- [Minimum Stein Discrepancy Estimators](https://mlsanity.com/paper/1906.08283/) (2019)
- [Stein Points](https://mlsanity.com/paper/1803.10161/) (2018)
- [Stochastic Stein Discrepancies](https://mlsanity.com/paper/2007.02857/) (2020)
- [Stein Variational Gradient Descent Without Gradient](https://mlsanity.com/paper/1806.02775/) (2018)
- [Message-Passing Monte Carlo: Generating low-discrepancy point sets via Graph Neural Networks](https://mlsanity.com/paper/2405.15059/) (2024)
- [Improving Efficiency of Sampling-based Motion Planning via Message-Passing Monte Carlo](https://mlsanity.com/paper/2410.03909/) (2024)

## Built on by (most cited first, 2 of 2)

- [Neural Low-Discrepancy Sequences](https://mlsanity.com/paper/2510.03745/) (2025)
- [Learning Geometric-Aware Quadrature Rules for Functional Minimization](https://mlsanity.com/paper/2508.05445/) (2025)

## 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.