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（GNN）已在多种图任务中取得显著性能。然而，现有GNN存在两个关键局限：其黑箱本质导致结果缺乏可解释性，且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，从高阶邻居中提取知识，并通过识别具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：一个用于图拓扑结构下复杂关系潜在表示的估计模型，以及一个可识别重要节点、边及关键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，并展示了其分层邻域混合的表征能力。我们利用模拟数据进行了全面的数值研究，证明MaGNet相较于多种最优替代方法具有更优性能。此外，我们将MaGNet应用于真实案例研究——从脑活动数据中提取任务关键信息，从而突显其在推进科学研究中的有效性。