Scalable and Robust Spatial Prediction via Multi-Resolution Ensembles of Predictive Processes

TL;DR

This paper introduces a multi-resolution ensemble approach for spatial prediction that balances scalability and accuracy, leveraging partitioning and robustness properties of predictive processes to handle large-scale data efficiently.

Contribution

It proposes a novel ensemble of predictive processes with spatial partitioning, enabling explicit control over the trade-off between computational efficiency and prediction accuracy.

Findings

Improved computational efficiency with large datasets.

Robustness to data contamination in spatial predictions.

Accurate predictions demonstrated in geostatistical applications.

Abstract

Gaussian processes provide a flexible framework for spatial prediction, but their computational cost limits applicability to large-scale data with large sample size $n$. Predictive processes (PPs), a popular low-rank approximation, mitigate this burden by projecting the original process onto a reduced set of $m\ll n$ inducing points. However, existing theory requires $m$ to grow with $n$, creating a trade-off between accuracy and computational efficiency. We address this challenge by introducing an ensemble of PPs based on spatial partitioning, and propose a novel partitioning and patching scheme with desirable properties. By generalizing the convergence results of PPs, it becomes possible to explicitly balance scalability and accuracy: increasing the number of ensemble components slows down the convergence but substantially improves computational efficiency. We further show theoretically that, despite the limited approximation accuracy of PPs with fixed $m$, they are asymptotically robust to data contamination. Motivated by this insight, we finally introduce a multi-resolution ensemble that combines PPs with fixed $m$ with multiple ensembles defined over possibly overlapping coarse to fine partitions. Simulations and large-scale geostatistical applications demonstrate that our approach delivers accurate, robust predictions with computational gains, providing a practical and broadly applicable solution for spatial prediction.