Comparing Initial Designs for Bayesian Optimization

• Activity Number: 28 - Computation, Design, and Quality Assurance of Physical Science and Engineering Applications
• Type: Contributed
• Date/Time: Sunday, August 8, 2021 : 1:30 PM to 3:20 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Kasia Dobrzycka* and Jon Stallrich
• Companies: North Carolina State University Statistics Department and North Carolina State
• Keywords: Gaussian Process; Latin Hypercube Design; Variable Selection; Space Filling; Distance Distributed; Optimization

Abstract

Space filling designs have been the accepted convention for initial samples in sequential designs for years. These designs are intuitively appealing because predictive methods often rely on borrowing nearby information and designs with good projection properties seem to support variable selection. However space filling designs may perform poorly in computer experiments because they do not clearly support estimation of the Gaussian Process hyperparameters, which impact prediction and variable selection. We propose that traditional space filling designs are actually not as effective as other proposed methods due to the nonparametric nature of Gaussian Process regression. We also question what design properties actually lead to effective estimation of Gaussian Process hyperparameters and whether projection properties actually lead to good variable selection properties in the context of Gaussian Process regression.