A new class of Markov random fields enabling lightweight sampling

TL;DR

This paper introduces a novel class of Markov random fields that leverage Gaussian Markov Random Fields for efficient sampling, achieving significant speed and energy savings while maintaining desirable properties.

Contribution

The work presents a new MRF class based on a mapping from GMRFs, enabling faster sampling with theoretical validation and practical efficiency improvements.

Findings

Sample at least 35x faster than Gibbs sampling

Use at least 37x less energy during sampling

Maintains empirical properties close to classical MRFs

Abstract

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.