Low Stein Discrepancy via Message-Passing Monte Carlo
This provides an incremental improvement in sampling methods for probabilistic modeling and machine learning applications.
The paper tackled the problem of sampling from multivariate probability distributions by extending Message-Passing Monte Carlo to minimize kernelized Stein discrepancy, resulting in Stein-MPMC outperforming methods like Stein Variational Gradient Descent and Stein Points with a lower Stein discrepancy.
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.