On the Use of Deep Neural Networks for Large-Scale Spatial Prediction

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.