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.

翻译：无向图模型为表示高维随机变量间的条件独立结构提供了基础框架。尽管无向图模型选择已成为高维统计学中的核心问题，但现有方法大多局限于参数化设定。本文提出一种基于扩散模型的非参数无向图模型选择方法。近期研究表明，扩散模型能够适应未知的底层分布图结构，但如何利用此类模型实现显式图估计仍未得到探索。为填补这一空白，我们提出了一种新颖的基于扩散模型的方法，用于实现非参数无向图模型选择。我们证明了所提方法的模型选择一致性，并通过大量模拟实验和两项真实数据分析展示了其实证性能。