基于扩散模型的非参数无向图模型选择
Nonparametric undirected graphical model selection using diffusion models
AI总结：
提出一种基于扩散模型的非参数方法用于无向图模型选择，证明了模型选择一致性，并通过模拟和实际数据分析验证了有效性。
摘要：
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本框架。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置。本文基于扩散模型，发展了一种非参数的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，但利用这些模型进行显式图估计仍未被探索。为填补这一空白，我们提出了一种新颖的基于扩散的非参数无向图模型选择方法。我们证明了所提方法的模型选择一致性，并通过大量模拟和两个实际数据分析展示了其实证性能。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
