In this manuscript we consider the problem of jointly estimating multiple graphical models in high dimensions. We assume that the data are collected from n subjects, each of which consists of T possibly dependent observations. The graphical models of subjects vary, but are assumed to change smoothly corresponding to a measure of closeness between subjects. We propose a kernel based method for jointly estimating all graphical models. Theoretically, under a double asymptotic framework, where both (T, n) and the dimension d can increase, we provide the explicit rate of convergence in parameter estimation. It characterizes the strength one can borrow across different individuals and the impact of data dependence on parameter estimation. Empirically, experiments on both synthetic and real resting state functional magnetic resonance imaging (rs-fMRI) data illustrate the effectiveness of the proposed method.

中文翻译：

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高维时间序列的多个图形模型的联合估计。


在这篇手稿中，我们考虑了联合估计高维多个图形模型的问题。我们假设数据是从 n 个受试者收集的，每个受试者都包含 T 个可能相关的观察结果。受试者的图形模型各不相同，但假设根据受试者之间的亲密程度而平滑变化。我们提出了一种基于内核的方法来联合估计所有图形模型。理论上，在双渐近框架下，（T，n）和维度 d 都可以增加，我们提供了参数估计的显式收敛率。它表征了可以在不同个体之间借用的力量以及数据依赖性对参数估计的影响。根据经验，合成和真实静息态功能磁共振成像（rs-fMRI）数据的实验证明了该方法的有效性。