Monotonic warpings for additive and deep Gaussian processes

Steven D. Barnett; Lauren J. Beesley; Annie S. Booth; Robert B. Gramacy; Dave Osthus

doi:10.1007/s11222-025-10598-7

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arXiv · 2408.01540

Monotonic warpings for additive and deep Gaussian processes

Steven D. Barnett·Lauren J. Beesley·Annie S. Booth·Robert B. Gramacy·Dave Osthus

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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.

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Steven D. Barnett, Lauren J. Beesley, Annie S. Booth, Robert B. Gramacy, Dave Osthus. 2024-08-02. Monotonic warpings for additive and deep Gaussian processes. https://doi.org/10.1007/s11222-025-10598-7

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