揭示克里金法与大神经网络的深层联系，提升模型可解释性与空间感知能力
The Connection between Kriging and Large Neural Networks
- 从概率论视角解析克里金法与神经网络的数学共性
- 发现二者在函数逼近与不确定性建模上存在本质相似性
- 适合关注模型可解释性与空间建模的研究者
人工智能已广泛渗透各学科领域，尤其在空间统计学中正与人工智能深度融合。本文探讨克里金法与神经网络之间的关联。尽管克里金法及其机器学习对应物高斯过程回归基于概率论与随机过程，而多数机器学习模型被视为黑箱，二者实则存在深刻联系。本文系统梳理相关文献，分析其内在关联。理解二者关系并融合两种视角，有望提升机器学习技术的可解释性、可靠性与空间感知能力。
原文摘要 · Abstract (English)
AI has impacted many disciplines and is nowadays ubiquitous. In particular, spatial statistics is in a pivotal moment where it will increasingly intertwine with AI. In this scenario, a relevant question is what relationship spatial statistics models have with machine learning (ML) models, if any. In particular, in this paper, we explore the connections between Kriging and neural networks. At first glance, they may appear unrelated. Kriging - and its ML counterpart, Gaussian process regression - are grounded in probability theory and stochastic processes, whereas many ML models are extensively considered Black-Box models. Nevertheless, they are strongly related. We study their connections and revisit the relevant literature. The understanding of their relations and the combination of both perspectives may enhance ML techniques by making them more interpretable, reliable, and spatially aware.
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