Constructing Large Nonstationary Spatio-Temporal Covariance Models via Compositional Warpings

TL;DR

This paper introduces a deep-learning-inspired method for constructing nonstationary spatio-temporal Gaussian process models by using compositional warpings, enabling better modeling of environmental phenomena with complex covariance structures.

Contribution

The paper proposes a novel approach to model nonstationary spatio-temporal covariance by composing simple warpings, improving flexibility and predictive performance over traditional stationary models.

Findings

The model captures covariance nonstationarity in space and time.

It provides better probabilistic predictions than stationary models.

Efficient fitting achieved with sparse linear algebra methods.

Abstract

Understanding and predicting environmental phenomena often requires the construction of spatio-temporal statistical models, which are typically Gaussian processes. A common assumption made on Gaussian processes is that of covariance stationarity, which is unrealistic in many geophysical applications. In this article, we introduce a deep-learning-inspired approach to construct descriptive nonstationary spatio-temporal models by modeling stationary processes on warped spatio-temporal domains. The warping functions we use are constructed using several simple injective warping units which, when combined through composition, can induce complex warpings. A stationary spatio-temporal covariance function on the warped domain induces covariance nonstationarity on the original domain. Sparse linear algebraic methods are used to reduce the computational complexity when fitting the model in a big data setting. We show that our proposed nonstationary spatio-temporal model can capture covariance nonstationarity in both space and time, and provide better probabilistic predictions than conventional stationary models in both simulation studies and on a real-world data set.