Exact Inference for Gaussian Process Regression in case of Big Data with   the Cartesian Product Structure
  Approximation algorithms are widely used in many engineering problems. To obtain a data set for approximation a factorial design of experiments is often used. In such case the size of the data set can be very large. Therefore, one of the most popular algorithms for approximation - Gaussian Process regression - can be hardly applied due to its computational complexity. In this paper a new approach for Gaussian Process regression in case of factorial design of experiments is proposed. It allows to efficiently compute exact inference and handle large multidimensional data sets. The proposed algorithm provides fast and accurate approximation and also handles anisotropic data. 
Mikhail Belyaev, Evgeny Burnaev and Yermek Kapushev
stat.ME math.ST stat.TH