Monotonic warpings for additive and deep Gaussian processes
Abstract
Gaussian processes (GPs) are canonical as surrogates for computer experiments because they enjoy a degree of analytic tractability. But that breaks when the response surface is constrained, say to be monotonic. Here, we provide a mono-GP construction for a single input that is highly efficient even though the calculations are non-analytic. Key ingredients include transformation of a reference process and elliptical slice sampling. We then show how mono-GP may be deployed effectively in two ways. One is additive, extending monotonicity to more inputs; the other is as a prior on injective latent warping variables in a deep Gaussian process for (non-monotonic, multi-input) non-stationary surrogate modeling. We provide illustrative and benchmarking examples throughout, showing that our methods yield improved performance over the state-of-the-art on examples from those two classes of problems.
Cite
@article{arxiv.2408.01540,
title = {Monotonic warpings for additive and deep Gaussian processes},
author = {Steven D. Barnett and Lauren J. Beesley and Annie S. Booth and Robert B. Gramacy and Dave Osthus},
journal= {arXiv preprint arXiv:2408.01540},
year = {2026}
}