Faster kriging: facing high-dimensional simulators

Kriging is one of the most widely used emulation methods in simulation. However, memory and time requirements potentially hinder its application to datasets generated by high-dimensional simulators. We borrow from the machine learning literature to propose a new algorithmic implementation of kriging that, while preserving prediction accuracy, notably reduces time and memory requirements. The theoretical and computational foundations of the algorithm are provided. The work then reports results of extensive numerical experiments to compare the performance of the proposed algorithm against current kriging implementations, on simulators of increasing dimensionality. Findings show notable savings in time and memory requirements that allow one to handle inputs in more that $10,000$ dimensions.