Herded Gibbs Sampling

TL;DR

Herded Gibbs is a deterministic variant of the Gibbs sampler with proven convergence rates for certain models, outperforming traditional Gibbs in image denoising and entity recognition tasks.

Contribution

The paper introduces herded Gibbs, a deterministic version of Gibbs sampling, with theoretical convergence guarantees and improved performance in specific applications.

Findings

Herded Gibbs achieves an $O(1/T)$ convergence rate for certain models.

Herded Gibbs outperforms traditional Gibbs in image denoising and entity recognition.

Convergence for sparsely connected models remains an open problem.

Abstract

The Gibbs sampler is one of the most popular algorithms for inference in statistical models. In this paper, we introduce a herding variant of this algorithm, called herded Gibbs, that is entirely deterministic. We prove that herded Gibbs has an $O(1/T)$ convergence rate for models with independent variables and for fully connected probabilistic graphical models. Herded Gibbs is shown to outperform Gibbs in the tasks of image denoising with MRFs and named entity recognition with CRFs. However, the convergence for herded Gibbs for sparsely connected probabilistic graphical models is still an open problem.