Quantifying uncertainty is crucial for robust and reliable predictions. However, existing spatiotemporal deep learning mostly focuses on deterministic prediction, overlooking the inherent uncertainty in such prediction. Particularly, highly-granular spatiotemporal datasets are often sparse, posing extra challenges in prediction and uncertainty quantification. To address these issues, this paper introduces a novel post-hoc Sparsity-awar Uncertainty Calibration (SAUC) framework, which calibrates uncertainty in both zero and non-zero values. To develop SAUC, we firstly modify the state-of-the-art deterministic spatiotemporal Graph Neural Networks (ST-GNNs) to probabilistic ones in the pre-calibration phase. Then we calibrate the probabilistic ST-GNNs for zero and non-zero values using quantile approaches.Through extensive experiments, we demonstrate that SAUC can effectively fit the variance of sparse data and generalize across two real-world spatiotemporal datasets at various granularities. Specifically, our empirical experiments show a 20\% reduction in calibration errors in zero entries on the sparse traffic accident and urban crime prediction. Overall, this work demonstrates the theoretical and empirical values of the SAUC framework, thus bridging a significant gap between uncertainty quantification and spatiotemporal prediction.

翻译：不确定性量化对于实现稳健可靠的预测至关重要。然而，现有的时空深度学习研究主要集中于确定性预测，忽视了此类预测中固有的不确定性。尤其值得注意的是，高粒度时空数据集通常具有稀疏性，这为预测和不确定性量化带来了额外的挑战。为解决这些问题，本文提出了一种新颖的事后稀疏感知不确定性校准（SAUC）框架，该框架能够同时对零值和非零值进行不确定性校准。为构建SAUC，我们首先在预校准阶段将最先进的确定性时空图神经网络（ST-GNNs）改进为概率性模型。随后，我们采用分位数方法对概率性ST-GNNs的零值和非零值进行校准。通过大量实验，我们证明SAUC能够有效拟合稀疏数据的方差，并在多种粒度的两个真实世界时空数据集上展现出良好的泛化能力。具体而言，我们的实证实验表明，在稀疏交通事故和城市犯罪预测任务中，零值条目的校准误差降低了20%。总体而言，本工作展示了SAUC框架的理论与实证价值，从而弥合了不确定性量化与时空预测之间的重要空白。