Deep learning is gaining increasing popularity for spatiotemporal forecasting. However, prior works have mostly focused on point estimates without quantifying the uncertainty of the predictions. In high stakes domains, being able to generate probabilistic forecasts with confidence intervals is critical to risk assessment and decision making. Hence, a systematic study of uncertainty quantification (UQ) methods for spatiotemporal forecasting is missing in the community. In this paper, we describe two types of spatiotemporal forecasting problems: regular grid-based and graph-based. Then we analyze UQ methods from both the Bayesian and the frequentist point of view, casting in a unified framework via statistical decision theory. Through extensive experiments on real-world road network traffic, epidemics, and air quality forecasting tasks, we reveal the statistical and computational trade-offs for different UQ methods: Bayesian methods are typically more robust in mean prediction, while confidence levels obtained from frequentist methods provide more extensive coverage over data variations. Computationally, quantile regression type methods are cheaper for a single confidence interval but require re-training for different intervals. Sampling based methods generate samples that can form multiple confidence intervals, albeit at a higher computational cost.
翻译:深层学习越来越受到时空预测的欢迎。然而,先前的工程大多集中在点估算上,而没有量化预测的不确定性。在高利贷领域,能够以信任间隔产生概率预测对于风险评估和决策至关重要。因此,在社区中缺乏对不确定性量化方法的系统研究,缺乏对空间时空预测方法的不确定性量化方法。在本文中,我们描述了两种周期性预测问题:常规网格和图形。然后,我们从巴伊西亚和经常点的角度分析UQ方法,通过统计决策理论在一个统一的框架内进行。通过对现实世界公路网络交通、流行病和空气质量预测任务的广泛实验,我们揭示了不同时空方法的统计和计算权衡:巴伊斯方法通常在平均预测中更加稳健,而从经常方法获得的信任水平则对数据变化提供更广泛的覆盖。计算,微弱回归型方法在单一信任间隔下比较便宜,但需要不同间隔的再培训。基于抽样的抽样可以形成多种信任间隔,尽管在成本间隔上进行计算。