  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.
