Journal of Data Science

Spatial data display correlation between observations collected at nearby locations. Generally, machine and deep learning methods either do not account for this correlation or do so indirectly through correlated features. To account for spatial correlation, we propose preprocessing the data using a spatial decorrelation transform motivated from properties of a multivariate Gaussian distribution and Vecchia approximations. The preprocessed, transformed data can then be ported into a machine or deep learning tool. After model fitting on the transformed data, the output can be spatially re-correlated via the corresponding inverse transformation. We show that including this spatial adjustment results in higher predictive accuracy on simulated and real spatial datasets.

For spatial kriging (prediction), the Gaussian process (GP) has been the go-to tool of spatial statisticians for decades. However, the GP is plagued by computational intractability, rendering it infeasible for use on large spatial data sets. Neural networks (NNs), on the other hand, have arisen as a flexible and computationally feasible approach for capturing nonlinear relationships. To date, however, NNs have only been scarcely used for problems in spatial statistics but their use is beginning to take root. In this work, we argue for equivalence between a NN and a GP and demonstrate how to implement NNs for kriging from large spatial data. We compare the computational efficacy and predictive power of NNs with that of GP approximations across a variety of big spatial Gaussian, non-Gaussian and binary data applications of up to size $n={10^{6}}$. Our results suggest that fully-connected NNs perform similarly to state-of-the-art, GP-approximated models for short-range predictions but can suffer for longer range predictions.