Selecting Optimal Variable Order in Autoregressive Ising Models

2026-02-23

AI Summary

This work addresses the critical dependence of autoregressive model performance on variable ordering, noting that suboptimal orderings can exacerbate the complexity of conditional distributions and degrade sample quality. To mitigate this issue, the paper introduces a graph-structure-aware optimal ordering strategy that, for the first time, integrates Markov Random Field (MRF) structure learning with autoregressive variable sequencing. By inferring the underlying MRF graph from data, the method guides variable ordering to simplify conditional dependencies. Experiments on the two-dimensional Ising model demonstrate that this approach substantially outperforms naive orderings, yielding generated samples with significantly higher fidelity. These results validate the effectiveness and superiority of structure-aware variable ordering for discrete data generation.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Reasoning under Uncertainty: Graphical Models
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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.

Problem

• autoregressive models
• variable ordering
• Ising models
• Markov random field
• conditional distributions

Innovation

• autoregressive models
• variable ordering
• Markov random field
• Ising model
• graphical model structure