# Constructing Large Nonstationary Spatio-Temporal Covariance Models via Compositional Warpings

arXiv: https://arxiv.org/abs/2202.03560 · HTML: https://mlsanity.com/paper/2202.03560/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2022.

## Built on by (most cited first, 4 of 4)

- [Statistical Deep Learning for Spatial and Spatio-Temporal Data](https://mlsanity.com/paper/2206.02218/) (2022)
- [Scalable Spatiotemporal Prediction with Bayesian Neural Fields](https://mlsanity.com/paper/2403.07657/) (2024)
- [Probabilistic Spatiotemporal Modeling of Day-Ahead Wind Power Generation with Input-Warped Gaussian Processes](https://mlsanity.com/paper/2409.16308/) (2024)
- [Modeling Nonstationary Extremal Dependence via Deep Spatial Deformations](https://mlsanity.com/paper/2505.12548/) (2025)

## Abstract (arXiv)

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.