Deep Gaussian Process Emulation using Stochastic Imputation

Abstract

Deep Gaussian processes (DGPs) provide a rich class of models that can better represent functions with varying regimes or sharp changes, compared to conventional GPs. In this work, we propose a novel inference method for DGPs for computer model emulation. By stochastically imputing the latent layers, our approach transforms a DGP into a linked GP: a novel emulator developed for systems of linked computer models. This transformation permits an efficient DGP training procedure that only involves optimizations of conventional GPs. In addition, predictions from DGP emulators can be made in a fast and analytically tractable manner by naturally using the closed form predictive means and variances of linked GP emulators. We demonstrate the method in a series of synthetic examples and empirical applications, and show that it is a competitive candidate for DGP surrogate inference, combining efficiency that is comparable to doubly stochastic variational inference and uncertainty quantification that is comparable to the fully-Bayesian approach. A Python package dgpsi implementing the method is also produced and available at https://github.com/mingdeyu/DGP.

Keywords:

• Elliptical slice sampling
• Linked Gaussian processes
• Option Greeks
• Surrogate model
• Stochastic expectation maximization

Supplementary Materials

Additional Examples and Results The file (supp˙results.pdf) contains an additional five-dimensional synthetic problem, a real-world example on aircraft engine model, and results for option Delta and Gamma of Section 5. (PDF file)

Code and Data The file (supp˙code.zip) contains codes and data used for synthetic and real-world examples in the manuscript and the supplement. It includes the version of the Python package dgpsi that produces the results in the manuscript and the supplementary materials. The latest and future versions of the package can be accessed via https://github.com/mingdeyu/DGP. (Zip file)

Acknowledgments

The authors would like to thank the Editor, an Associate Editor, and two referees for their insightful comments that help improve the quality of the work.

Disclosure Statement

The authors report that there are no competing interests to declare.