Geostatistical Learning: Challenges and Opportunities

TL;DR

This paper discusses the unique challenges of applying statistical learning in geospatial contexts, highlighting issues like spatial correlation and covariate shifts, and evaluates existing error estimation methods which are often inadequate.

Contribution

It introduces the geostatistical learning problem, assesses current error estimation methods in geospatial settings, and offers practical guidelines amidst ongoing research for better solutions.

Findings

Existing error estimation methods are inadequate for geospatial data.

Spatial correlation and covariate shift significantly impact model generalization.

Guidelines are provided for model selection in geospatial machine learning.

Abstract

Statistical learning theory provides the foundation to applied machine learning, and its various successful applications in computer vision, natural language processing and other scientific domains. The theory, however, does not take into account the unique challenges of performing statistical learning in geospatial settings. For instance, it is well known that model errors cannot be assumed to be independent and identically distributed in geospatial (a.k.a. regionalized) variables due to spatial correlation; and trends caused by geophysical processes lead to covariate shifts between the domain where the model was trained and the domain where it will be applied, which in turn harm the use of classical learning methodologies that rely on random samples of the data. In this work, we introduce the geostatistical (transfer) learning problem, and illustrate the challenges of learning from geospatial data by assessing widely-used methods for estimating generalization error of learning models, under covariate shift and spatial correlation. Experiments with synthetic Gaussian process data as well as with real data from geophysical surveys in New Zealand indicate that none of the methods are adequate for model selection in a geospatial context. We provide general guidelines regarding the choice of these methods in practice while new methods are being actively researched.