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

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 involve two major challenges. First, spatial processes with exogenous variables are highly non-stationary and characterized by a heterogeneous covariance structure. Second, because of the large numbers of observations present, it is inefficient to apply full Kriging. In order to handle heterogeneity in covariance and 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 a procedure to find the optimal hyperplanes. To alleviate the problem of discontinuity in the global predictor, we impose continuity constraints on the boundaries of the neighboring subdomains. Numerical experiments demonstrate that SPLK outperforms, or is comparable to, the algorithms commonly applied to spatial datasets.