Projecting Ising Model Parameters for Fast Mixing

TL;DR

This paper introduces an algorithm to project Ising model parameters onto a set that guarantees fast mixing, improving sampling accuracy in models with strong interactions and limited sampling time.

Contribution

The authors propose a novel parameter projection method for Ising models that ensures rapid mixing, addressing intractability issues in high treewidth scenarios.

Findings

Projected parameters enable faster mixing in Ising models.

Gibbs sampling with projected parameters is more accurate under strong interactions.

The method improves sampling efficiency when time is limited.

Abstract

Inference in general Ising models is difficult, due to high treewidth making tree-based algorithms intractable. Moreover, when interactions are strong, Gibbs sampling may take exponential time to converge to the stationary distribution. We present an algorithm to project Ising model parameters onto a parameter set that is guaranteed to be fast mixing, under several divergences. We find that Gibbs sampling using the projected parameters is more accurate than with the original parameters when interaction strengths are strong and when limited time is available for sampling.