Functional data has become a commonly encountered data type. In this paper, we contribute to the literature on functional graphical modelling by extending the notion of conditional Gaussian Graphical models and proposing a double-penalized estimator by which to recover the edge-set of the corresponding graph. Penalty parameters play a crucial role in determining the precision matrices for the response variables and the regression matrices. The performance and model selection process in the proposed framework are investigated using information criteria. Moreover, we propose a novel version of the Kullback-Leibler cross-validation designed for conditional joint Gaussian Graphical Models. The evaluation of model performance is done in terms of Kullback-Leibler divergence and graph recovery power.

翻译：功能数据已成为一种常见的数据类型。本文通过扩展条件高斯图模型的概念，并提出一种双重惩罚估计量来恢复相应图的边集，从而为功能图建模文献做出贡献。惩罚参数在确定响应变量的精度矩阵和回归矩阵中起着关键作用。本文利用信息准则研究了所提框架的性能和模型选择过程。此外，我们提出了一种针对条件联合高斯图模型的新型Kullback-Leibler交叉验证方法。模型性能的评估基于Kullback-Leibler散度和图恢复能力。