Graph Neural Networks (GNNs) have emerged as powerful tools for predicting outcomes in graph-structured data. However, a notable limitation of GNNs is their inability to provide robust uncertainty estimates, which undermines their reliability in contexts where errors are costly. One way to address this issue is by providing prediction sets that contain the true label with a predefined probability margin. Our approach builds upon conformal prediction (CP), a framework that promises to construct statistically robust prediction sets or intervals. There are two primary challenges: first, given dependent data like graphs, it is unclear whether the critical assumption in CP - exchangeability - still holds when applied to node classification. Second, even if the exchangeability assumption is valid for conformalized link prediction, we need to ensure high efficiency, i.e., the resulting prediction set or the interval length is small enough to provide useful information. In this article, we propose a novel approach termed Robust Conformal Prediction for GNNs (RoCP-GNN), which integrates conformal prediction (CP) directly into the GNN training process. This method generates prediction sets, instead of just point predictions, that are valid at a user-defined confidence level, assuming only exchangeability. Our approach robustly predicts outcomes with any predictive GNN model while quantifying the uncertainty in predictions within the realm of graph-based semi-supervised learning (SSL). Experimental results demonstrate that GNN models with size loss provide a statistically significant increase in performance. We validate our approach on standard graph benchmark datasets by coupling it with various state-of-the-art GNNs in node classification. The code will be made available after publication.

翻译：图神经网络（GNNs）已成为预测图结构数据结果的有力工具。然而，GNNs的一个显著局限是无法提供鲁棒的不确定性估计，这在错误代价高昂的应用场景中削弱了其可靠性。解决该问题的一种途径是提供以预定概率边界包含真实标签的预测集。我们的方法建立在共形预测（CP）框架之上，该框架旨在构建统计上鲁棒的预测集或区间。当前面临两个主要挑战：首先，对于图这类具有依赖关系的数据，应用于节点分类时CP的核心假设——可交换性——是否依然成立尚不明确。其次，即使可交换性假设在共形化链接预测中成立，仍需保证高效性，即所得预测集或区间长度足够小以提供有效信息。本文提出一种称为鲁棒图神经网络共形预测（RoCP-GNN）的新方法，将共形预测直接集成到GNN训练过程中。该方法在仅假设可交换性的前提下，生成满足用户定义置信水平的预测集（而非仅点预测）。我们的方法能够鲁棒地结合任意预测性GNN模型输出结果，并在基于图的半监督学习（SSL）框架内量化预测不确定性。实验结果表明，采用尺寸损失的GNN模型在性能上实现了统计显著提升。我们通过在标准图基准数据集上耦合多种前沿GNN节点分类模型验证了该方法的有效性。代码将在论文发表后公开。