Motivated by the problem of inferring the graph structure of functional connectivity networks from multi-level functional magnetic resonance imaging data, we develop a valid inference framework for high-dimensional graphical models that accounts for group-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. Specifically, we propose a LASSO-based estimator and a de-biased LASSO-based inference framework for the fixed effect parameters in the doubly high-dimensional linear mixed model, leveraging random matrix theory to deal with challenges induced by the identical fixed and random effect design matrices arising in our setting. Moreover, we introduce consistent estimators for the variance components to identify subject-specific edges in the inferred graph. To illustrate the generality of the proposed approach, we also adapt our method to account for serial correlation by learning heterogeneous graphs in the setting of a vector autoregressive model. We demonstrate the performance of the proposed framework using real data and benchmark simulation studies.

翻译：受从多层次功能磁共振成像数据推断功能连接网络图结构问题的驱动，我们开发了一种考虑群体异质性的高维图模型有效推断框架。我们提出基于邻域的方法来学习图结构，并将该问题重新表述为双重高维线性混合模型中固定效应参数的推断问题。具体而言，我们针对双重高维线性混合模型中的固定效应参数，提出基于LASSO的估计量及去偏LASSO推断框架，并利用随机矩阵理论应对因固定效应与随机效应设计矩阵相同（本文设定下）所引发的挑战。此外，我们引入方差分量的一致估计量以识别推断图中的主体特定边。为展示所提方法的普适性，我们还通过向量自回归模型设置下的异质图学习适配了该方法以处理序列相关性。我们通过真实数据与基准仿真研究验证了所提框架的性能。