Deep Compositional Spatial Models

by   Andrew Zammit Mangion, et al.

Nonstationary, anisotropic spatial processes are often used when modelling, analysing and predicting complex environmental phenomena. One such class of processes considers a stationary, isotropic process on a warped spatial domain. The warping function is generally difficult to fit and not constrained to be bijective, often resulting in 'space-folding.' Here, we propose modelling a bijective warping function through a composition of multiple elemental bijective 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. Inspired by recent methodological and technological advances in deep learning and deep Gaussian processes, we employ approximate Bayesian methods to make inference with these models using graphical processing units. Through simulation studies in one and two dimensions we show that the deep compositional spatial models are quick to fit, and are able to provide better predictions and uncertainty quantification than other deep stochastic models of similar complexity. We also show their remarkable capacity to model highly nonstationary, anisotropic spatial data using radiances from the MODIS instrument aboard the Aqua satellite.



There are no comments yet.



Constructing Large Nonstationary Spatio-Temporal Covariance Models via Compositional Warpings

Understanding and predicting environmental phenomena often requires the ...

Modeling Nonstationary and Asymmetric Multivariate Spatial Covariances via Deformations

Multivariate spatial-statistical models are useful for modeling environm...

Random Feature Expansions for Deep Gaussian Processes

The composition of multiple Gaussian Processes as a Deep Gaussian Proces...

Compositionally-Warped Gaussian Processes

The Gaussian process (GP) is a nonparametric prior distribution over fun...

Computationally Efficient Deep Bayesian Unit-Level Modeling of Survey Data under Informative Sampling for Small Area Estimation

The topic of deep learning has seen a surge of interest in recent years ...

Modelling spatial heterogeneity and discontinuities using Voronoi tessellations

Many methods for modelling spatial processes assume global smoothness pr...

Deep Learning for Spatiotemporal Modeling of Urbanization

Urbanization has a strong impact on the health and wellbeing of populati...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.