Accurate uncertainty quantification in graph neural networks (GNNs) is essential, especially in high-stakes domains where GNNs are frequently employed. Conformal prediction (CP) offers a promising framework for quantifying uncertainty by providing $\textit{valid}$ prediction sets for any black-box model. CP ensures formal probabilistic guarantees that a prediction set contains a true label with a desired probability. However, the size of prediction sets, known as $\textit{inefficiency}$, is influenced by the underlying model and data generating process. On the other hand, Bayesian learning also provides a credible region based on the estimated posterior distribution, but this region is $\textit{well-calibrated}$ only when the model is correctly specified. Building on a recent work that introduced a scaling parameter for constructing valid credible regions from posterior estimate, our study explores the advantages of incorporating a temperature parameter into Bayesian GNNs within CP framework. We empirically demonstrate the existence of temperatures that result in more efficient prediction sets. Furthermore, we conduct an analysis to identify the factors contributing to inefficiency and offer valuable insights into the relationship between CP performance and model calibration.

翻译：图神经网络中的精确不确定性量化至关重要，特别是在高频使用GNN的高风险领域。共形预测（CP）通过为任意黑箱模型提供$\textit{有效}$预测集，为不确定性量化提供了有前景的框架。CP确保预测集以期望概率包含真实标签的正式概率保证。然而，预测集的大小（称为$\textit{低效性}$）受底层模型和数据生成过程的影响。另一方面，贝叶斯学习也基于估计的后验分布提供可信区域，但该区域仅在模型正确指定时才能实现$\textit{良好校准}$。基于近期引入缩放参数以从后验估计构建有效可信区域的研究，本文探讨了在CP框架下将温度参数融入贝叶斯GNN的优势。我们通过实验证明，存在某些温度可生成更高效的预测集。此外，我们通过分析识别导致低效性的因素，并为CP性能与模型校准之间的关系提供有价值的见解。