Liu Qihai, Lee Kevin H, Kang Hyun Bin
Department of Statistics, Western Michigan University, Kalamazoo, MI, United States of America.
PLoS One. 2025 Jan 2;20(1):e0316458. doi: 10.1371/journal.pone.0316458. eCollection 2025.
Graphical models have been widely used to explicitly capture the statistical relationships among the variables of interest in the form of a graph. The central question in these models is to infer significant conditional dependencies or independencies from high-dimensional data. In the current literature, it is common to assume that the high-dimensional data come from a homogeneous source and follow a parametric graphical model. However, in real-world context the observed data often come from different sources and may have heterogeneous dependencies across the whole population. In addition, for time-dependent data, many work has been done to estimate discrete correlation structures at each time point but less work has been done to estimate global correlation structures over all time points. In this work, we propose finite mixtures of functional graphical models (MFGM), which detect the heterogeneous subgroups of the population and estimate single graph for each subgroup by considering the correlation structures. We further design an estimation method for MFGM using an iterative Expectation-Maximization (EM) algorithm and functional graphical lasso (fglasso). Numerically, we demonstrate the performance of our method in simulation studies and apply our method to high-dimensional electroencephalogram (EEG) dataset taken from an alcoholism study.
图形模型已被广泛用于以图形的形式明确捕捉感兴趣变量之间的统计关系。这些模型中的核心问题是从高维数据中推断出显著的条件依赖性或独立性。在当前文献中，通常假设高维数据来自同质源并遵循参数化图形模型。然而，在现实世界中，观测数据往往来自不同的源，并且在整个人口中可能具有异质依赖性。此外，对于时间相关数据，已经做了很多工作来估计每个时间点的离散相关结构，但在估计所有时间点上的全局相关结构方面所做的工作较少。在这项工作中，我们提出了功能图形模型的有限混合（MFGM），它通过考虑相关结构来检测人群中的异质子组并为每个子组估计单个图形。我们进一步使用迭代期望最大化（EM）算法和功能图形套索（fglasso）设计了一种MFGM估计方法。在数值上，我们在模拟研究中展示了我们方法的性能，并将我们的方法应用于取自酒精中毒研究的高维脑电图（EEG）数据集。
