Joint Estimation of Multiple Graphical Models from High Dimensional Time Series.
Joint Estimation of Multiple Graphical Models from High Dimensional Time Series.
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DOI：
10.1111/rssb.12123
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发表时间：
2016-03-01
期刊：
影响因子：
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通讯作者：
Caffo B
中科院分区：
文献类型：
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作者：
Qiu H;Han F;Liu H;Caffo B
在本手稿中，我们考虑了在高维度中共同估计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，每个受试者都由t可能取决于观察结果。受试者的图形模型有所不同，但假定会平稳地对应于受试者之间的亲密度。我们提出了一种基于内核的方法，用于共同估计所有图形模型。从理论上讲，在双渐近框架下，（t，n）和尺寸d都可以增加，我们在参数估计中提供了明确的收敛速率。它表征了一个人可以借用不同个体的强度以及数据依赖对参数估计的影响。从经验上讲，对合成和真实静止状态功能磁共振成像（RS-FMRI）数据的实验说明了所提出方法的有效性。
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.