Fast covariance parameter estimation of spatial Gaussian process models using neural networks

Gaussian processes (GPs) are a popular model for spatially referenced data\nand allow descriptive statements, predictions at new locations, and simulation\nof new fields. Often a few parameters are sufficient to parameterize the\ncovariance function, and maximum likelihood (ML) methods can be used to\nestimate these parameters from data. ML methods, however, are computationally\ndemanding. For example, in the case of local likelihood estimation, even\nfitting covariance models on modest size windows can overwhelm typical\ncomputational resources for data analysis. This limitation motivates the idea\nof using neural network (NN) methods to approximate ML estimates. We train NNs\nto take moderate size spatial fields or variograms as input and return the\nrange and noise-to-signal covariance parameters. Once trained, the NNs provide\nestimates with a similar accuracy compared to ML estimation and at a speedup by\na factor of 100 or more. Although we focus on a specific covariance estimation\nproblem motivated by a climate science application, this work can be easily\nextended to other, more complex, spatial problems and provides a\nproof-of-concept for this use of machine learning in computational statistics.\n