Functional graphical models explore dependence relationships of random processes. This is achieved through estimating the precision matrix of the coefficients from the Karhunen-Loeve expansion. This paper deals with the problem of estimating functional graphs that consist of the same random processes and share some of the dependence structure. By estimating a single graph we would be shrouding the uniqueness of different sub groups within the data. By estimating a different graph for each sub group we would be dividing our sample size. Instead, we propose a method that allows joint estimation of the graphs while taking into account the intrinsic differences of each sub group. This is achieved by a hierarchical penalty that first penalizes on a common level and then on an individual level. We develop a computation method for our estimator that deals with the non-convex nature of the objective function. We compare the performance of our method with existing ones on a number of different simulated scenarios. We apply our method to an EEG data set that consists of an alcoholic and a non-alcoholic group, to construct brain networks.

翻译：功能图形模型探索随机过程的依附关系。 这是通过估计Karhunen-Loev 扩展系数的精确矩阵实现的。 本文涉及估算由相同随机过程组成的功能图的问题, 并分享部分依附结构。 通过估算单个图形, 我们将覆盖数据中不同子组的独特性。 通过估算每个子组的不同图形, 我们将会区分我们的样本大小。 相反, 我们建议一种方法, 允许在计算每个子组内在差异的同时对图表进行联合估算。 这是通过先在共同层次然后在单个层次上处罚的等级处罚来实现的。 我们为我们的估算器开发一种计算方法, 处理客观函数的非电解特性。 我们用我们的方法与现有方法的性能对不同模拟情景进行对比。 我们用我们的方法对由酒精和非酒精组构成的电离组数据集进行计算, 以构建大脑网络 。