Ordered conditional approximation of Potts models

TL;DR

This paper introduces fast ordered conditional approximation methods for Potts models, enabling efficient inference and sampling in large spatial fields with linear complexity and parallelizable computations.

Contribution

It presents a novel approximation technique for Potts models that significantly reduces computational complexity and facilitates rapid inference and sampling.

Findings

Methods are linear in the number of locations.

Approach enables direct sampling from approximate joint distribution.

Demonstrated on simulated data and satellite imagery.

Abstract

Potts models, which can be used to analyze dependent observations on a lattice, have seen widespread application in a variety of areas, including statistical mechanics, neuroscience, and quantum computing. To address the intractability of Potts likelihoods for large spatial fields, we propose fast ordered conditional approximations that enable rapid inference for observed and hidden Potts models. Our methods can be used to directly obtain samples from the approximate joint distribution of an entire Potts field. The computational complexity of our approximation methods is linear in the number of spatial locations; in addition, some of the necessary computations are naturally parallel. We illustrate the advantages of our approach using simulated data and a satellite image.