Spatial Deep Convolutional Neural Networks

TL;DR

This paper introduces a novel convolutional neural network approach using tailored spatial basis functions for improved accuracy in spatial prediction tasks, addressing computational challenges of traditional Gaussian process models.

Contribution

It develops a new method integrating spatial basis functions into CNNs, enhancing prediction accuracy and efficiency for complex spatial data.

Findings

Outperforms existing spatial prediction methods in accuracy.

Demonstrates effectiveness on both simulated and real datasets.

Provides a framework for uncertainty quantification in spatial predictions.

Abstract

Spatial prediction problems often use Gaussian process models, which can be computationally burdensome in high dimensions. Specification of an appropriate covariance function for the model can be challenging when complex non-stationarities exist. Recent work has shown that pre-computed spatial basis functions and a feed-forward neural network can capture complex spatial dependence structures while remaining computationally efficient. This paper builds on this literature by tailoring spatial basis functions for use in convolutional neural networks. Through both simulated and real data, we demonstrate that this approach yields more accurate spatial predictions than existing methods. Uncertainty quantification is also considered.