On Mixing in Pairwise Markov Random Fields with Application to Social Networks

TL;DR

This paper investigates the mixing properties of pairwise Markov random fields, providing conditions for rapid mixing and methods for perfect simulation, with applications to social networks and other domains.

Contribution

It offers new conditions for rapid mixing of Glauber dynamics and introduces a monotone perfect simulation approach for submodular energy functions.

Findings

Conditions for rapid mixing of Glauber dynamics established

Constructed a monotone perfect simulation method

Applicable to social network models with attributes

Abstract

We consider pairwise Markov random fields which have a number of important applications in statistical physics, image processing and machine learning such as Ising model and labeling problem to name a couple. Our own motivation comes from the need to produce synthetic models for social networks with attributes. First, we give conditions for rapid mixing of the associated Glauber dynamics and consider interesting particular cases. Then, for pairwise Markov random fields with submodular energy functions we construct monotone perfect simulation.