Faster Kriging: Facing High-Dimensional Simulators

AbstractHow can one make a large and complex model fast and “small”? The simulation literature has extensively addressed this problem, and the kriging method has proven to be one of the most successful methods to deal with complex simulators. In “Facing High-Dimensional Simulators: Faster Kriging?,” Xuefei Lu, Alessandro Rudi, Emanuele Borgonovo, and Lorenzo Rosasco propose a new kriging implementation, called “fast kriging,” that copes with dimensionality issues, allowing one to deal with data sets coming from simulators with thousands of inputs.Kriging is one of the most widely used emulation methods in simulation. However, memory and time requirements potentially hinder its application to data sets 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 across more that 10,000 dimensions.