Active Learning for Deep Gaussian Process Surrogates

TL;DR

This paper introduces a novel active learning framework using Deep Gaussian Processes with a new Bayesian inference scheme, enabling efficient surrogate modeling of complex simulation responses with limited data.

Contribution

It develops an active learning approach for DGPs incorporating elliptical slice sampling for Bayesian inference, improving efficiency and uncertainty quantification in surrogate modeling.

Findings

Effective on simulation and real data experiments

Reduces training data and computational costs

Maintains accuracy with small datasets

Abstract

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.