Exploring the Efficacy of Statistical and Deep Learning Methods for Large Spatial Datasets: A Case Study

TL;DR

This paper evaluates statistical and deep learning methods for large spatial datasets, ultimately favoring the Vecchia approximation, and demonstrates their effectiveness through a competition and real data application.

Contribution

The study introduces new R functions for Gaussian process modeling, compares multiple approaches, and applies them to large spatial datasets, winning two sub-competitions.

Findings

Vecchia approximation outperformed other methods in the competition

Developed R functions to support zero-mean Gaussian processes and uncertainty estimation

Proved the effectiveness of the proposed methods on real satellite data

Abstract

Increasingly large and complex spatial datasets pose massive inferential challenges due to high computational and storage costs. Our study is motivated by the KAUST Competition on Large Spatial Datasets 2023, which tasked participants with estimating spatial covariance-related parameters and predicting values at testing sites, along with uncertainty estimates. We compared various statistical and deep learning approaches through cross-validation and ultimately selected the Vecchia approximation technique for model fitting. To overcome the constraints in the R package GpGp, which lacked support for fitting zero-mean Gaussian processes and direct uncertainty estimation-two things that are necessary for the competition, we developed additional \texttt{R} functions. Besides, we implemented certain subsampling-based approximations and parametric smoothing for skewed sampling distributions of the estimators. Our team DesiBoys secured victory in two out of four sub-competitions, validating the effectiveness of our proposed strategies. Moreover, we extended our evaluation to a large real spatial satellite-derived dataset on total precipitable water, where we compared the predictive performances of different models using multiple diagnostics.