We consider a novel problem, bi-level graphical modeling, in which multiple individual graphical models can be considered as variants of a common group-level graphical model and inference of both the group- and individual-level graphical models is of interest. Such a problem arises from many applications, including multi-subject neuro-imaging and genomics data analysis. We propose a novel and efficient statistical method, the random covariance model, to learn the group- and individual-level graphical models simultaneously. The proposed method can be nicely interpreted as a random covariance model that mimics the random effects model for mean structures in linear regression. It accounts for similarity between individual graphical models, identifies group-level connections that are shared by individuals, and simultaneously infers multiple individual-level networks. Compared to existing multiple graphical modeling methods that only focus on individual-level graphical modeling, our model learns the group-level structure underlying the multiple individual graphical models and enjoys computational efficiency that is particularly attractive for practical use. We further define a measure of degrees-of-freedom for the complexity of the model useful for model selection. We demonstrate the asymptotic properties of our method and show its finite-sample performance through simulation studies. Finally, we apply the method to our motivating clinical data, a multi-subject resting-state functional magnetic resonance imaging dataset collected from participants diagnosed with schizophrenia, identifying both individual- and group-level graphical models of functional connectivity.

中文翻译：

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用于静息态 fMRI 数据的双层图形建模的随机协方差模型

我们考虑一个新的问题，双层图形建模，其中多个单独的图形模型可以被认为是一个常见的组级图形模型的变体，并且对组级和个人级图形模型的推断是有意义的。这样的问题来自许多应用，包括多学科神经成像和基因组学数据分析。我们提出了一种新颖有效的统计方法，即随机协方差模型，以同时学习组级和个体级图形模型。所提出的方法可以很好地解释为随机协方差模型，该模型模拟线性回归中平均结构的随机效应模型。它考虑了个体图形模型之间的相似性，识别个体共享的组级连接，并同时推断出多个个体级网络。与现有的仅关注个体级图形建模的多图形建模方法相比，我们的模型学习了多个个体图形模型背后的组级结构，并且具有对实际应用特别有吸引力的计算效率。我们进一步定义了对模型选择有用的模型复杂性的自由度度量。我们证明了我们方法的渐近特性，并通过模拟研究展示了它的有限样本性能。最后，我们将该方法应用于我们的激励临床数据，这是从被诊断患有精神分裂症的参与者收集的多主体静息状态功能磁共振成像数据集，