Graphical models, used to express conditional dependence between random variables observed at various nodes, are used extensively in many fields such as genetics, neuroscience, and social network analysis. While most current statistical methods for estimating graphical models focus on scalar data, there is interest in estimating analogous dependence structures when the data observed at each node are functional, such as signals or images. In this paper, we propose a fully Bayesian regularization scheme for estimating functional graphical models. We first consider a direct Bayesian analog of the functional graphical lasso proposed by Qiao et al. (2019). We then propose a regularization strategy via the graphical horseshoe. We compare these approaches via simulation study and apply our proposed functional graphical horseshoe to two motivating applications, electroencephalography data for comparing brain activation between an alcoholic group and controls, as well as changes in structural connectivity in the presence of traumatic brain injury (TBI). Our results yield insight into how the brain attempts to compensate for disconnected networks after injury.
翻译:图形模型用来表示在不同节点观测到的随机变量之间的有条件依赖性,在遗传学、神经科学和社会网络分析等许多领域广泛使用。虽然目前用于估算图形模型的大多数统计方法都侧重于标量数据,但当每个节点观测到的数据具有功能时,例如信号或图像等,人们有兴趣估计类似的依赖结构。在本文中,我们提出了一个完全的巴伊西亚正规化方案,用于估算功能图形模型。我们首先考虑基奥等人(2019年)提议的功能图形拉索(Lasso)直接比喻。我们随后通过图形马蹄学提出了正规化战略。我们通过模拟研究对这些方法进行比较,并将我们提议的功能图形马蹄用于两种激励应用程序,即电子脑摄影数据,以比较酒精组和控制之间的脑活性,以及在出现创伤性脑损伤时结构连接的变化(TBI)。我们的结果有助于深入了解大脑如何试图在受伤后对断开的网络进行补偿。