Uncertainty Propagation in Deep Gaussian Process Networks

Abstract This work presents a deep Gaussian process model for spatial interpolation. The model consists of an irregular network where each node is a Gaussian process whose output is a full Gaussian distribution, as opposed to the single value provided by standard deep neural networks. Each node integrates the uncertainty in its parent nodes analytically through the use of a specialized non-stationary covariance function. The network is capable of modelling multiple variables, even of different types, and its construction allows the imputation of external knowledge, such as lithologically constrained grades and correlations. A special node based on stochastic differential equations learns non-stationary patterns automatically by warping the input space. The model is applied to a time series and two- and three-dimensional cases. An open-source implementation in Python is available.