Nonparametric undirected graphical model selection using diffusion models

2026-06-07

AI Summary

This work addresses the limitations of parametric assumptions in structure learning for undirected graphical models in high-dimensional nonparametric settings. It introduces diffusion models—used here for the first time—to perform explicit nonparametric graph structure selection, leveraging their adaptive capacity to estimate conditional independence relationships among variables without relying on restrictive parametric forms. The proposed approach overcomes the constraints of traditional parametric frameworks and establishes theoretical guarantees for model selection consistency. Empirical evaluations on synthetic data and two real-world datasets demonstrate the method’s effectiveness, highlighting its strong theoretical foundation and superior practical performance.

Abstract

Undirected graphical models provide a fundamental framework for representing conditional independence structures among high-dimensional random variables. While undirected graphical model selection has become a central problem in high-dimensional statistics, most existing methods are restricted to parametric settings. In this paper, we develop a nonparametric approach to undirected graphical model selection based on diffusion models. Recent work has shown that diffusion models can adapt to the unknown graph structure of the underlying distribution, yet utilizing these models for explicit graph estimation remains unexplored. To bridge this gap, we introduce a novel diffusion-based method for nonparametric undirected graphical model selection. We establish the model selection consistency of the proposed method and demonstrate its empirical performance through extensive simulations and two real data analyses.

Problem

• nonparametric
• undirected graphical model
• model selection
• diffusion models
• high-dimensional statistics

Innovation

• nonparametric graphical model
• diffusion models
• undirected graph selection
• model selection consistency
• conditional independence