Probabilistic Duality for Parallel Gibbs Sampling without Graph Coloring

TL;DR

This paper introduces a probabilistic duality concept enabling highly parallel Gibbs sampling for complex graphical models, especially useful in dynamic or densely connected networks where traditional methods struggle.

Contribution

The paper proposes a novel probabilistic duality framework that facilitates parallel Gibbs sampling without graph coloring, suitable for dynamic and densely connected models.

Findings

Enables parallel Gibbs sampling with minimal preprocessing.

Improves applicability to dynamic and densely connected networks.

Offers a trade-off with slower mixing times compared to sequential methods.

Abstract

We present a new notion of probabilistic duality for random variables involving mixture distributions. Using this notion, we show how to implement a highly-parallelizable Gibbs sampler for weakly coupled discrete pairwise graphical models with strictly positive factors that requires almost no preprocessing and is easy to implement. Moreover, we show how our method can be combined with blocking to improve mixing. Even though our method leads to inferior mixing times compared to a sequential Gibbs sampler, we argue that our method is still very useful for large dynamic networks, where factors are added and removed on a continuous basis, as it is hard to maintain a graph coloring in this setup. Similarly, our method is useful for parallelizing Gibbs sampling in graphical models that do not allow for graph colorings with a small number of colors such as densely connected graphs.