Deep Compositional Spatial Models

Understand

Spatial processes with nonstationary and anisotropic covariance structure are often used when modelling, analysing and predicting complex environmental phenomena.

• Such processes may often be expressed as ones that have stationary and isotropic covariance structure on a warped spatial domain.
• However, the warping function is generally difficult to fit and not constrained to be injective, often resulting in `space-folding.' Here, we propose modelling an injective warping function through a composition of multiple elemental injective functions in a deep-learning framework.
• We consider two cases; first, when these functions are known up to some weights that need to be estimated, and, second, when the weights in each layer are random.