Abstract

We introduce a statistical graphical model for multivariate functional data, which are common in medical applications such as EEG and fMRI. Recently published functional graphical models rely on the multivariate Gaussian process assumption, but we relax it by introducing the functional copula Gaussian graphical model (FCGGM). This model removes the marginal Gaussian assumption but retains the simplicity of the Gaussian dependence structure, which is particularly attractive for large data. We develop four estimators for the FCGGM and establish the consistency and the convergence rates of one of them. We compare our FCGGM with the existing functional Gaussian graphical model by simulations, and apply our method to an EEG dataset to construct brain networks. Supplementary materials for this article are available online.

摘要

我们引入了多变量功能数据的统计图形模型，这在 EEG 和 fMRI 等医学应用中很常见。最近发表的函数图模型依赖于多元高斯过程假设，但我们通过引入函数 copula 高斯图模型 (FCGGM) 来放松它。该模型去除了边际高斯假设，但保留了高斯依赖结构的简单性，这对于大数据特别有吸引力。我们为 FCGGM 开发了四个估计器，并确定了其中一个的一致性和收敛速度。我们通过模拟将我们的 FCGGM 与现有的功能高斯图形模型进行比较，并将我们的方法应用于 EEG 数据集以构建大脑网络。本文的补充材料可在线获取。