Graph Neural Networks (GNNs) have achieved promising performance in a variety of graph-focused tasks. Despite their success, however, existing GNNs suffer from two significant limitations: a lack of interpretability in their results due to their black-box nature, and an inability to learn representations of varying orders. To tackle these issues, we propose a novel Model-agnostic Graph Neural Network (MaGNet) framework, which is able to effectively integrate information of various orders, extract knowledge from high-order neighbors, and provide meaningful and interpretable results by identifying influential compact graph structures. In particular, MaGNet consists of two components: an estimation model for the latent representation of complex relationships under graph topology, and an interpretation model that identifies influential nodes, edges, and node features. Theoretically, we establish the generalization error bound for MaGNet via empirical Rademacher complexity, and demonstrate its power to represent layer-wise neighborhood mixing. We conduct comprehensive numerical studies using simulated data to demonstrate the superior performance of MaGNet in comparison to several state-of-the-art alternatives. Furthermore, we apply MaGNet to a real-world case study aimed at extracting task-critical information from brain activity data, thereby highlighting its effectiveness in advancing scientific research.

翻译：图神经网络（GNNs）在各类以图为中心的任务中已展现出优异的性能。然而，尽管取得了成功，现有GNN仍存在两个显著局限：由于其黑箱性质导致结果缺乏可解释性，以及无法学习不同阶数的表示。为解决这些问题，我们提出了一种新颖的模型无关图神经网络（MaGNet）框架，该框架能够有效整合多阶信息、从高阶邻居中提取知识，并通过识别有影响力的紧凑图结构提供有意义且可解释的结果。具体而言，MaGNet包含两个组件：用于估计图拓扑下复杂关系潜在表示的估计模型，以及用于识别关键节点、边与节点特征的解释模型。在理论上，我们通过经验Rademacher复杂度建立了MaGNet的泛化误差界，并证明了其表示逐层邻域混合的能力。我们使用模拟数据进行了全面的数值研究，证明MaGNet相较于多种前沿方法具有更优越的性能。此外，我们将MaGNet应用于一项旨在从脑活动数据中提取任务关键信息的真实案例研究，从而彰显其在推动科学研究方面的有效性。