The Connection between Kriging and Large Neural Networks

TL;DR

This paper explores the theoretical connections between Kriging, a spatial statistics method, and neural networks, aiming to enhance machine learning interpretability and spatial awareness by integrating these approaches.

Contribution

It investigates the relationship between Kriging and neural networks, providing insights that could improve ML interpretability and spatial modeling capabilities.

Findings

Kriging and neural networks are fundamentally related through probabilistic frameworks.

Understanding their connection can lead to more interpretable ML models.

Combining both approaches may enhance spatial awareness in machine learning.

Abstract

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.