Low Stein Discrepancy via Message-Passing Monte Carlo

Nathan Kirk, T. Konstantin Rusch, Jakob Zech, Daniela Rus

Keywords: stein discrepancy, sampling, message-passing monte carlo, graph neural networks, geometric deep learning, low-discrepancy

Abstract: 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 $F$ 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.

Submission Number: 52