Spatial data display correlation between observations collected at neighboring locations. Generally, machine and deep learning methods either do not account for this correlation or do so indirectly through correlated features and thereby forfeit predictive accuracy. To remedy this shortcoming, we propose preprocessing the data using a spatial decorrelation transform derived from properties of a multivariate Gaussian distribution and Vecchia approximations. The transformed data can then be ported into a machine or deep learning tool. After model fitting on the transformed data, the output can be spatially re-correlated via the corresponding inverse transformation. We show that including this spatial adjustment results in higher predictive accuracy on simulated and real spatial datasets.

翻译：空间数据在相邻位置采集的观测值之间表现出相关性。通常，机器学习和深度学习方法要么未考虑这种相关性，要么仅通过相关特征间接处理，从而牺牲了预测精度。为弥补这一不足，我们提出基于多元高斯分布特性与Vecchia近似推导空间去相关变换对数据进行预处理。变换后的数据可输入至机器学习或深度学习工具中。在变换数据上完成模型拟合后，可通过对应的逆变换对输出结果进行空间重相关处理。我们通过模拟与真实空间数据集的实验证明，引入这种空间调整机制能有效提升预测精度。