A novel approach for Markov Random Field with intractable normalising constant on large lattices

TL;DR

This paper introduces a new scalable method for estimating Markov Random Fields on large lattices that avoids computing intractable normalising constants, offering efficiency and competitive accuracy.

Contribution

The paper presents a recursive decomposition approach leveraging conditional independence to estimate Markov Random Fields efficiently on large lattices, bypassing the normalising constant.

Findings

Method has computational complexity O(N) for N pixels.

Performs well in simulations compared to exact likelihood methods.

Effective on very large lattice datasets.

Abstract

The pseudo likelihood method of Besag(1974), has remained a popular method for estimating Markov random field on a very large lattice, despite various documented deficiencies. This is partly because it remains the only computationally tractable method for large lattices. We introduce a novel method to estimate Markov random fields defined on a regular lattice. The method takes advantage of conditional independence structures and recursively decomposes a large lattice into smaller sublattices. An approximation is made at each decomposition. Doing so completely avoids the need to compute the troublesome normalising constant. The computational complexity is $O(N)$, where $N$ is the the number of pixels in lattice, making it computationally attractive for very large lattices. We show through simulation, that the proposed method performs well, even when compared to the methods using exact likelihoods.