Active Discrimination Learning for Gaussian Process Models

TL;DR

This paper develops methods for designing experiments to effectively discriminate between two Gaussian process models, using sequential and static criteria based on divergence measures and covariance distances, with theoretical and numerical analysis.

Contribution

It introduces new criteria and frameworks for optimal experimental design to distinguish Gaussian process models, including computationally simpler distance-based measures.

Findings

Sequential design based on divergence maximization improves discrimination.

New static criteria like Fréchet distance are effective and easier to compute.

Numerical illustrations demonstrate the practical benefits of proposed methods.

Abstract

The paper covers the design and analysis of experiments to discriminate between two Gaussian process models, 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 Fr\'echet 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.