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Approximation algorithms are widely used in many engineering problems. Toobtain a data set for approximation a factorial design of experiments is oftenused. In such case the size of the data set can be very large. Therefore, oneof the most popular algorithms for approximation - Gaussian Process regression- can be hardly applied due to its computational complexity. In this paper anew approach for Gaussian Process regression in case of factorial design ofexperiments is proposed. It allows to efficiently compute exact inference andhandle large multidimensional data sets. The proposed algorithm provides fastand accurate approximation and also handles anisotropic data.

Exact Inference for Gaussian Process Regression in case of Big Data with the Cartesian Product Structure