Active Learning for Deep Gaussian Process Surrogates
This work addresses the problem of efficiently building surrogate models for expensive computer simulations, which is relevant for researchers and engineers who rely on such simulations for design and analysis.
This paper explores Deep Gaussian Processes (DGPs) as surrogates for computer simulation experiments, leveraging their non-stationary flexibility and uncertainty quantification. By integrating a novel elliptical slice sampling (ESS) Bayesian posterior inference with active learning (AL) strategies, the authors demonstrate that their framework can effectively build sequential designs with smaller training sets, reducing computational costs.
Deep Gaussian processes (DGPs) are increasingly popular as predictive models in machine learning (ML) for their non-stationary flexibility and ability to cope with abrupt regime changes in training data. Here we explore DGPs as surrogates for computer simulation experiments whose response surfaces exhibit similar characteristics. In particular, we transport a DGP's automatic warping of the input space and full uncertainty quantification (UQ), via a novel elliptical slice sampling (ESS) Bayesian posterior inferential scheme, through to active learning (AL) strategies that distribute runs non-uniformly in the input space -- something an ordinary (stationary) GP could not do. Building up the design sequentially in this way allows smaller training sets, limiting both expensive evaluation of the simulator code and mitigating cubic costs of DGP inference. When training data sizes are kept small through careful acquisition, and with parsimonious layout of latent layers, the framework can be both effective and computationally tractable. Our methods are illustrated on simulation data and two real computer experiments of varying input dimensionality. We provide an open source implementation in the "deepgp" package on CRAN.