Selecting Optimal Variable Order in Autoregressive Ising Models

TL;DR

This paper introduces a method to improve autoregressive Ising models by learning the underlying graph structure to determine optimal variable orderings, resulting in more accurate sampling.

Contribution

It presents a novel approach that leverages learned graphical models to optimize variable orderings in autoregressive models, reducing complexity and enhancing sample quality.

Findings

Graph-informed orderings improve sample fidelity.

Structure-aware orderings reduce conditioning set size.

Numerical experiments confirm higher accuracy.

Abstract

Autoregressive models enable tractable sampling from learned probability distributions, but their performance critically depends on the variable ordering used in the factorization via complexities of the resulting conditional distributions. We propose to learn the Markov random field describing the underlying data, and use the inferred graphical model structure to construct optimized variable orderings. We illustrate our approach on two-dimensional image-like models where a structure-aware ordering leads to restricted conditioning sets, thereby reducing model complexity. Numerical experiments on Ising models with discrete data demonstrate that graph-informed orderings yield higher-fidelity generated samples compared to naive variable orderings.