Sparse Pseudo-input Local Kriging for Large Spatial Datasets with Exogenous Variables

TL;DR

This paper introduces SPLK, a scalable spatial prediction method that partitions large datasets into subdomains with hyperplanes, applying sparse Kriging locally to efficiently model spatial processes with exogenous variables.

Contribution

The paper proposes a novel SPLK method that uses hyperplanes for domain partitioning and local sparse Kriging, improving scalability and capturing heterogeneity in large spatial datasets.

Findings

SPLK outperforms existing methods in numerical experiments.

SPLK effectively captures heterogeneity through regional parameter tuning.

The method maintains continuity across subdomain boundaries.

Abstract

We study large-scale spatial systems that contain exogenous variables, e.g. environmental factors that are significant predictors in spatial processes. Building predictive models for such processes is challenging because the large numbers of observations present makes it inefficient to apply full Kriging. In order to reduce computational complexity, this paper proposes Sparse Pseudo-input Local Kriging (SPLK), which utilizes hyperplanes to partition a domain into smaller subdomains and then applies a sparse approximation of the full Kriging to each subdomain. We also develop an optimization procedure to find the desired hyperplanes. To alleviate the problem of discontinuity in the global predictor, we impose continuity constraints on the boundaries of the neighboring subdomains. Furthermore, partitioning the domain into smaller subdomains makes it possible to use different parameter values for the covariance function in each region and, therefore, the heterogeneity in the data structure can be effectively captured. Numerical experiments demonstrate that SPLK outperforms, or is comparable to, the algorithms commonly applied to spatial datasets.