Fitting Gaussian Processes (GPs) provides interpretable aleatoric uncertainty quantification for estimation of spatio-temporal fields. Spatio-temporal deep learning models, while scalable, typically assume a simplistic independent covariance matrix for the response, failing to capture the underlying correlation structure. However, spatio-temporal GPs suffer from issues of scalability and various forms of approximation bias resulting from restrictive assumptions of the covariance kernel function. We propose STACI, a novel framework consisting of a variational Bayesian neural network approximation of non-stationary spatio-temporal GP along with a novel spatio-temporal conformal inference algorithm. STACI is highly scalable, taking advantage of GPU training capabilities for neural network models, and provides statistically valid prediction intervals for uncertainty quantification. STACI outperforms competing GPs and deep methods in accurately approximating spatio-temporal processes and we show it easily scales to datasets with millions of observations.

翻译：拟合高斯过程为时空场估计提供了可解释的偶然性不确定性量化。尽管时空深度学习模型具有可扩展性，但其通常假设响应具有简单的独立协方差矩阵，未能捕捉潜在的关联结构。然而，时空高斯过程存在可扩展性问题，以及由协方差核函数的限制性假设导致的各种近似偏差。我们提出了STACI这一新颖框架，它包含非平稳时空高斯过程的变分贝叶斯神经网络近似方法，以及一种创新的时空保形推断算法。STACI具有高度可扩展性，能够利用神经网络模型的GPU训练能力，并提供统计有效的预测区间以进行不确定性量化。STACI在精确近似时空过程方面优于竞争性高斯过程和深度学习方法，并且我们证明其能够轻松扩展到包含数百万观测值的数据集。