Graph Neural Networks (GNNs) have achieved promising performance in a variety of graph-focused tasks. Despite their success, existing GNNs suffer from two significant limitations: a lack of interpretability in 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 sequentially 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 important node features. Theoretically, we establish the generalization error bound for MaGNet via empirical Rademacher complexity, and showcase 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）在多种基于图的任务中取得了显著性能。尽管取得了成功，现有GNN仍存在两个重要局限：由于其黑箱特性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，我们提出一种新颖的模型无关图神经网络（MaGNet）框架，该框架能够顺序整合不同阶数的信息，从高阶邻域中提取知识，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：一个用于估计图拓扑结构下复杂关系潜在表示的估计模型，以及一个用于识别关键节点、边及重要节点特征的解释模型。理论上，我们通过经验Rademacher复杂度建立了MaGNet的泛化误差界，并展示了其在表示逐层邻域混合方面的能力。我们使用模拟数据进行了全面的数值研究，证明MaGNet相较于多种最先进替代方法具有更优性能。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实际案例研究，从而凸显其在推动科学研究方面的有效性。