Low Stein Discrepancy via Message-Passing Monte Carlo
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866913761022967808 |
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| author | Kirk, Nathan Rusch, T. Konstantin Zech, Jakob Rus, Daniela |
| author_facet | Kirk, Nathan Rusch, T. Konstantin Zech, Jakob Rus, Daniela |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21103 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Low Stein Discrepancy via Message-Passing Monte Carlo Kirk, Nathan Rusch, T. Konstantin Zech, Jakob Rus, Daniela Machine Learning Numerical Analysis 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. |
| title | Low Stein Discrepancy via Message-Passing Monte Carlo |
| topic | Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2503.21103 |