Analysis of dimension reduction in Gaussian process regression

• Activity Number: 487 - Design and Analysis of Computer Experiments for Complex Systems
• Type: Invited
• Date/Time: Wednesday, August 2, 2017 : 10:30 AM to 12:20 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Minyong Lee* and Art Owen
• Companies: Stanford University and Stanford University
• Keywords: Gaussian process regression ; dimension Reduction ; computer experiments

Abstract

Dimension reduction methods in regression are widely used for analyzing high dimensional computer experiments. In this work, we analyze the quality of dimension reduction in computer experiments, using projected Gaussian processes. We propose a Gaussian process model on the original function that produces a tractable Gaussian process on the dimensionally reduced space. We translate the length-scale hyperparameters in the Gaussian process regression to the importance of the variables. We quantify the proportional variance of the Gaussian process explained by the dimensionally reduced space. This helps us choose the dimension of the dimensionally reduced space.