Statistical relational learning (SRL) and graph neural networks (GNNs) are two powerful approaches for learning and inference over graphs. Typically, they are evaluated in terms of simple metrics such as accuracy over individual node labels. Complex aggregate graph queries (AGQ) involving multiple nodes, edges, and labels are common in the graph mining community and are used to estimate important network properties such as social cohesion and influence. While graph mining algorithms support AGQs, they typically do not take into account uncertainty, or when they do, make simplifying assumptions and do not build full probabilistic models. In this paper, we examine the performance of SRL and GNNs on AGQs over graphs with partially observed node labels. We show that, not surprisingly, inferring the unobserved node labels as a first step and then evaluating the queries on the fully observed graph can lead to sub-optimal estimates, and that a better approach is to compute these queries as an expectation under the joint distribution. We propose a sampling framework to tractably compute the expected values of AGQs. Motivated by the analysis of subgroup cohesion in social networks, we propose a suite of AGQs that estimate the community structure in graphs. In our empirical evaluation, we show that by estimating these queries as an expectation, SRL-based approaches yield up to a 50-fold reduction in average error when compared to existing GNN-based approaches.

统计关系学习 (SRL) 和图神经网络 (GNN) 是两种强大的图学习和推理方法。通常，它们是根据简单的指标（例如单个节点标签的准确性）进行评估的。复杂的聚合图查询(AGQ) 涉及多个节点、边和标签在图挖掘社区中很常见，用于估计重要的网络属性，例如社会凝聚力和影响力。尽管图挖掘算法支持 AGQ，但它们通常不考虑不确定性，或者在考虑不确定性时，会做出简化假设并且不构建完整的概率模型。在本文中，我们在具有部分观察节点标签的图上检查了 SRL 和 GNN 在 AGQ 上的性能。我们表明，毫不奇怪，推断未观察到的节点标签作为第一步，然后在完全观察到的图上评估查询可能会导致次优估计，并且更好的方法是将这些查询计算为联合下的期望分配。我们提出了一个采样框架来轻松计算 AGQ 的期望值。受对社交网络中子群凝聚力分析的启发，我们提出了一套 AGQ，用于估计图中的社区结构。在我们的实证评估中，我们表明，通过将这些查询估计为期望值，与现有的基于 GNN 的方法相比，基于 SRL 的方法的平均误差降低了 50 倍。