This work addresses the problem of efficient sampling of Markov random fields (MRF). The sampling of Potts or Ising MRF is most often based on Gibbs sampling, and is thus computationally expensive. We consider in this work how to circumvent this bottleneck through a link with Gaussian Markov Random fields. The latter can be sampled in several cost-effective ways, and we introduce a mapping from real-valued GMRF to discrete-valued MRF. The resulting new class of MRF benefits from a few theoretical properties that validate the new model. Numerical results show the drastic performance gain in terms of computational efficiency, as we sample at least 35x faster than Gibbs sampling using at least 37x less energy, all the while exhibiting empirical properties close to classical MRFs.

翻译：本研究致力于解决马尔可夫随机场（MRF）的高效采样问题。Potts或Ising MRF的采样通常基于吉布斯采样，计算成本高昂。本文探讨如何通过建立与高斯马尔可夫随机场（GMRF）的关联来规避这一瓶颈。后者可通过多种经济高效的方式进行采样，我们提出了一种从实值GMRF到离散值MRF的映射方法。由此产生的新型MRF类别具有若干理论特性，验证了新模型的有效性。数值结果表明，在计算效率方面实现了显著提升：与吉布斯采样相比，采样速度至少提升35倍，能耗至少降低37倍，同时保持与经典MRF相近的经验特性。