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：图神经网络中的不确定性量化至关重要，尤其是在高风险领域中频繁使用图神经网络的场景。共形预测通过为任意黑箱模型提供$\textit{有效}$预测集，为量化不确定性提供了一个有前景的框架。CP确保正式的概率保证，即预测集以期望概率包含真实标签。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$\textit{良好校准}$。基于近期一项引入缩放参数以从后验估计构建有效可信区域的工作，我们的研究探讨了在CP框架下将温度参数纳入贝叶斯图神经网络的优点。我们通过实验证明了存在导致更高效预测集的温度值。此外，我们进行了分析以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了宝贵见解。