Discrimination between Gaussian process models: active learning and static constructions

The paper covers the design and analysis of experiments to discriminate between two Gaussian process models with different covariance kernels, such as those widely used in computer experiments, kriging, sensor location and machine learning. Two frameworks are considered. First, we study sequential constructions, where successive design (observation) points are selected, either as additional points to an existing design or from the beginning of observation. The selection relies on the maximisation of the difference between the symmetric Kullback Leibler divergences for the two models, which depends on the observations, or on the mean squared error of both models, which does not. Then, we consider static criteria, such as the familiar log-likelihood ratios and the Frechet distance between the covariance functions of the two models. Other distance-based criteria, simpler to compute than previous ones, are also introduced, for which, considering the framework of approximate design, a necessary condition for the optimality of a design measure is provided. The paper includes a study of the mathematical links between different criteria and numerical illustrations are provided.

Automated summary

This paper discusses the design and analysis of experiments to distinguish between Gaussian process models with different covariance kernels. Two frameworks are explored: sequential constructions and static criteria. The selection of observation points in sequential constructions is based on the maximization of the difference between symmetric Kullback Leibler divergences or the mean squared error of the models. Static criteria include log-likelihood ratios, Frechet distance, and other distance-based criteria. The paper also examines the mathematical links between different criteria and provides numerical illustrations.