The analysis of data such as graphs has been gaining increasing attention in the past years. This is justified by the numerous applications in which they appear. Several methods are present to predict graphs, but much fewer to quantify the uncertainty of the prediction. The present work proposes an uncertainty quantification methodology for graphs, based on conformal prediction. The method works both for graphs with the same set of nodes (labelled graphs) and graphs with no clear correspondence between the set of nodes across the observed graphs (unlabelled graphs). The unlabelled case is dealt with the creation of prediction sets embedded in a quotient space. The proposed method does not rely on distributional assumptions, it achieves finite-sample validity, and it identifies interpretable prediction sets. To explore the features of this novel forecasting technique, we perform two simulation studies to show the methodology in both the labelled and the unlabelled case. We showcase the applicability of the method in analysing the performance of different teams during the FIFA 2018 football world championship via their player passing networks.

翻译：近年来，图等数据的分析日益受到关注，这归因于其广泛的应用场景。目前已有多种图预测方法，但针对预测不确定性的量化研究相对较少。本文基于共形预测方法，提出了一种面向图的预测不确定性量化框架。该方法既能处理具有相同节点集合的图（标记图），也能处理观测图中节点集合无明确对应关系的图（未标记图）。针对未标记情形，通过在商空间中嵌入预测集实现处理。该方法无需分布假设，可保证有限样本有效性，并能生成可解释的预测集。为探索这一新型预测技术的特性，我们通过两项仿真研究分别验证了标记图与未标记图中的方法性能。最后，以2018年FIFA世界杯足球锦标赛中不同球队的球员传球网络为例，展示了该方法在团队表现分析中的适用性。