Nearest-Neighbor Neural Networks for Geostatistics

Abstract: Kriging is the predominant method used for spatial prediction, but relies on the assumption that predictions are linear combinations of the observations. Kriging often also relies on additional assumptions such as normality and stationarity. We propose a more flexible spatial prediction method based on the Nearest-Neighbor Neural Network (4N) process that embeds deep learning into a geostatistical model. We show that the 4N process is a valid stochastic process and propose a series of new ways to construct features to be used as inputs to the deep learning model based on neighboring information. Our model framework outperforms some existing state-of-art geostatistical modelling methods for simulated non-Gaussian data and is applied to a massive forestry dataset.