Discrimination between Gaussian process models: active learning and static constructions

Area of Science:

• Statistics
• Machine Learning
• Experimental Design

Background:

• Gaussian process models with varying covariance kernels are fundamental in computer experiments, kriging, sensor placement, and machine learning.
• Discriminating between these models is crucial for accurate predictions and reliable analysis.

Purpose of the Study:

• To develop and analyze experimental designs for effectively discriminating between two Gaussian process models.
• To compare sequential and static design criteria for model selection.

Main Methods:

• Investigated sequential design strategies based on maximizing Kullback-Leibler divergence or minimizing mean squared error.
• Examined static criteria including log-likelihood ratios and Fréchet distance.
• Introduced novel, computationally simpler distance-based criteria and derived optimality conditions for approximate designs.

Main Results:

• Established mathematical relationships between various discrimination criteria.
• Provided numerical illustrations demonstrating the performance of the proposed methods.
• Identified necessary conditions for optimal design measures in approximate design settings.

Conclusions:

• The study offers a comprehensive framework for designing experiments to differentiate Gaussian process models.
• The proposed methods and criteria enhance the efficiency and accuracy of model selection in various scientific and engineering applications.