A research on application of inverse estimation by Gaussian process regression to computer experiments

Abstract

In computer experiments, we often collect sample data by space filling designs, and analyze relationship between response and factors using Gaussian process regression. This approach is believed effective in predicting response level from factor levels. The focus of this research is inverse estimation that is to find factor levels from the given response level. In inverse estimation problem, there is a need to evaluate the effectiveness of the combination of space filling design and Gaussian process regression. We focus on sample size in space filling design and hyper parameter of kernel function in Gaussian process regression. Some results of evaluation are introduced, such as accuracy of inverse estimates between space filling design and Gaussian process regression. We discuss the influence of hyper parameter level of kernel function, that is also important as same as the influence of sample size in space filling design in some cases. The suggested number of samples can be more than ten times of the number of factors, where ten times is suggested as guideline for prediction problem of Gaussian process regression in previous study. We need to determine hyper parameter level in each model, and sample size thinking cost of computer experiments.