  There has been a great deal of recent interest in the development of spatial
prediction algorithms for very large datasets and/or prediction domains. These
methods have primarily been developed in the spatial statistics community, but
there has been growing interest in the machine learning community for such
methods, primarily driven by the success of deep Gaussian process regression
approaches and deep convolutional neural networks. These methods are often
computationally expensive to train and implement and consequently, there has
been a resurgence of interest in random projections and deep learning models
based on random weights -- so called reservoir computing methods. Here, we
combine several of these ideas to develop the Random Ensemble Deep Spatial
(REDS) approach to predict spatial data. The procedure uses random Fourier
features as inputs to an extreme learning machine (a deep neural model with
random weights), and with calibrated ensembles of outputs from this model based
on different random weights, it provides a simple uncertainty quantification.
The REDS method is demonstrated on simulated data and on a classic large
satellite data set.
