Abstract

We develop a high-dimensional graphical modeling approach for functional data where the number of functions exceeds the available sample size. This is accomplished by proposing a sparse estimator for a concentration matrix when identifying linear manifolds. As such, the procedure extends the ideas of the manifold representation for functional data to high-dimensional settings where the number of functions is larger than the sample size. By working in a penalized setting it enriches the functional data framework by estimating sparse undirected graphs that show how functional nodes connect to other functional nodes. The procedure allows multiple coarseness scales to be present in the data and proposes a simultaneous estimation of several related graphs. Its performance is illustrated using a real-life fMRI dataset and with simulated data.

摘要

我们为函数数量超过可用样本大小的函数数据开发了一种高维图形建模方法。这是通过在识别线性流形时提出浓度矩阵的稀疏估计器来实现的。因此，该过程将函数数据的流形表示的思想扩展到函数数量大于样本大小的高维设置。通过在惩罚设置中工作，它通过估计稀疏无向图来丰富功能数据框架，这些无向图显示功能节点如何连接到其他功能节点。该过程允许数据中存在多个粗糙度尺度，并提出对几个相关图的同时估计。使用现实生活中的功能磁共振成像数据集和模拟数据来说明其性能。