Machine learning and geostatistics are two fundamentally different frameworks for predicting and spatially mapping soil properties. Geostatistics leverages the spatial structure of soil properties, while machine learning captures the relationship between available environmental features and soil properties. We propose a hybrid framework that enriches ML with spatial context through engineering of 'spatial lag' features from ordinary kriging. We call this approach 'kriging prior regression' (KpR), as it follows the inverse logic of regression kriging. To evaluate this approach, we assessed both the point and probabilistic prediction performance of KpR, using the TabPFN model across six fieldscale datasets from LimeSoDa. These datasets included soil organic carbon, clay content, and pH, along with features derived from remote sensing and in-situ proximal soil sensing. KpR with TabPFN demonstrated reliable uncertainty estimates and more accurate predictions in comparison to several other spatial techniques (e.g., regression/residual kriging with TabPFN), as well as to established non-spatial machine learning algorithms (e.g., random forest). Most notably, it significantly improved the average R2 by around 30% compared to machine learning algorithms without spatial context. This improvement was due to the strong prediction performance of the TabPFN algorithm itself and the complementary spatial information provided by KpR features. TabPFN is particularly effective for prediction tasks with small sample sizes, common in precision agriculture, whereas KpR can compensate for weak relationships between sensing features and soil properties when proximal soil sensing data are limited. Hence, we conclude that KpR with TabPFN is a very robust and versatile modelling framework for digital soil mapping in precision agriculture.

翻译：机器学习和地统计学是用于预测和空间制图土壤性质的两种根本不同的框架。地统计学利用土壤性质的空间结构，而机器学习则捕捉可用环境特征与土壤性质之间的关系。我们提出了一种混合框架，通过从普通克里金中构建“空间滞后”特征，为机器学习模型赋予空间上下文信息。我们将这种方法称为“克里金先验回归”（KpR），因为它遵循回归克里金的逆逻辑。为评估此方法，我们使用TabPFN模型在来自LimeSoDa的六个田间尺度数据集上，评估了KpR的点预测和概率预测性能。这些数据集包括土壤有机碳、粘土含量和pH值，以及来自遥感和原位近端土壤传感的特征。与其它几种空间技术（例如，使用TabPFN的回归/残差克里金）以及成熟的非空间机器学习算法（例如，随机森林）相比，结合TabPFN的KpR展示了可靠的不确定性估计和更准确的预测。最值得注意的是，与没有空间上下文的机器学习算法相比，它显著提高了平均R2约30%。这一改进归因于TabPFN算法本身强大的预测性能以及KpR特征提供的补充空间信息。TabPFN对于样本量较小的预测任务特别有效，这在精准农业中很常见，而KpR可以在近端土壤传感数据有限时，补偿传感特征与土壤性质之间较弱的关系。因此，我们得出结论：结合TabPFN的KpR是精准农业中数字土壤制图的一个非常稳健且多功能的建模框架。