Convolutional Methods for Predictive Modeling of Geospatial Data
Tyler Wilson, Pang‐Ning Tan, Lifeng Luo · Society for Industrial and Applied Mathematics eBooks · 2020
Convolutional methods are useful for modeling geospatial data as they enable the extraction of broad-scale spatial patterns from the local attributes observed at each location. The weighted aggregation performed by the convolutional operator also helps to smoothen the noisy data collected at the given locations. However, current convolutional methods are primarily designed to learn the spatial dependencies of the input (predictor) variables only. The recent success in applying multi-task learning to various geospatial prediction problems shows that the model parameters themselves may also be spatially related. This suggests the possibility of employing convolutional methods to learn the spatial dependencies among the model parameters at different locations, especially in situations where there are limited training data available to fit accurate local models. In this paper, we investigate three different ways to incorporate convolutions into geospatial prediction models—convolutions on the predictors, model parameters, or a hybrid of both. We provide guidance on when convolution of each type can be fruitfully applied and verify their effectiveness using both synthetic and real-world datasets.