Gaussian Process Models in Spatial Data Mining

Naren Ramakrishnan

Abstract

Gaussian processes (GPs) are local approximation techniques that model spatial data by placing (and updating) priors on the covariance structures underlying the data. Originally developed for geo-spatial contexts, they are also applicable in general contexts that involve computing and modeling with multi-level spatial aggregates, e.g., modeling a configuration space for crystallographic design, casting folding energies as a function of a protein’s contact map, and formulation of vaccination policies taking into account social dynamics of individuals. Typically, we assume a parametrized covariance structure underlying the data to be modeled. We estimate the covariance parameters conditional on the locations for which we have observed data, and use the inferred structure to make predictions at new locations. GPs have a probabilistic basis that allow us to estimate variances at unsampled locations, aiding in the design of targeted sampling strategies.