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.

翻译：统计学习理论为应用机器学习及其在计算机视觉、自然语言处理和其他科学领域的各种成功应用奠定了基础。但是,理论没有考虑到在地理空间环境中进行统计学习的独特挑战。例如,众所周知,由于空间相关性,模型错误不能被假定为独立和在地理空间(a.k.a.区域化)变量中以相同方式分布;地球物理过程导致的趋势导致模型所培训的领域和将应用的领域之间发生共变,这反过来又损害了依赖随机数据样本的经典学习方法的使用。在这项工作中,我们引入了地理统计学(转移)学习问题,并说明了通过评估广泛使用的估算学习模型一般错误的方法、在可变式转移和空间相关性下从地理空间数据中学习的挑战。与合成高斯进程数据以及新西兰地球物理调查中的真实数据进行的实验表明,这些方法没有一个足以用于在地理空间空间环境中选择模型。我们为这些方法的实际选择提供了一般准则,同时正在积极研究新方法。