Learning with Partition of Unity-based Kriging Estimators

For supervised regression tasks we propose and study a new tool, namely Kriging Estimator based on the Partition of Unity (KEPU) method. Its background belongs to the framework of local kernel-based interpolation methods. Indeed, even if the latter needs to be accurately tailored for gaussian process regression, the KEPU scheme provides a global estimator which is constructed by gluing together the local Kriging predictors via compactly supported weights. The added value of this investigation is twofold. On the one hand, our theoretical studies about the propagation of the uncertainties from the local predictors to the global one offer the opportunity to define the PU method in a stochastic framework and hence to provide confidence intervals for the PU approximant. On the other hand, as confirmed by extensive numerical experiments, when the number of instances grows, such a method enables us to significantly reduce the usually high complexity cost of fitting via gaussian processes.