使用双重高维线性混合模型进行异质图模型的推断
Inference for Heterogeneous Graphical Models using Doubly High-Dimensional Linear-Mixed Models
AI总结：
针对多水平功能磁共振成像数据中的功能连接网络，提出基于双重高维线性混合模型的去偏LASSO推断框架，利用随机矩阵理论处理组级异质性，并扩展至向量自回归模型，通过真实数据和模拟验证性能。
摘要：
受从多水平功能磁共振成像数据中推断功能连接网络图结构问题的启发，我们开发了一个有效的推断框架，用于考虑组级异质性的高维图模型。我们引入了一种基于邻域的方法来学习图结构，并将问题重新表述为在双重高维线性混合模型中推断固定效应参数。具体来说，我们提出了一种基于LASSO的估计器和一种去偏LASSO的推断框架，用于双重高维线性混合模型中的固定效应参数，利用随机矩阵理论来应对由我们设置中相同的固定和随机效应设计矩阵引起的挑战。此外，我们引入了方差分量的一致估计器，以识别推断图中的受试者特定边。为了说明所提出方法的通用性，我们还调整了我们的方法以考虑序列相关性，通过在向量自回归模型的设置中学习异质图。我们使用真实数据和基准模拟研究来展示所提出框架的性能。
英文摘要：
Inferring the structure of population-level functional connectivity networks from multi-subject functional magnetic resonance imaging data is essential for understanding the connectivity patterns underlying cognitive and behavioral functions. Graphical models provide a formal statistical framework for inferring the graph structure. However, the multi-level nature of functional magnetic resonance imaging data---where each level corresponds, for instance, to a subject---compromises the inferential validity of most existing methods. In this paper, we develop a valid inference framework for high-dimensional graphical models that accounts for cross-level heterogeneity. We introduce a neighborhood-based method to learn the graph structure and reframe the problem as that of inferring fixed effect parameters in a doubly high-dimensional linear mixed model. We then propose a LASSO-based estimator and a de-biased LASSO-based inference framework for these fixed effect parameters. We evaluate the performance of the proposed framework using benchmark simulation studies and apply it to descriptively compare graph structures between the functional connectivity networks of two predefined groups of subjects from the Human Connectome Project.
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