Monotonic warpings for additive and deep Gaussian processes

Fuente: arXiv
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Main Authors: Barnett, Steven D., Beesley, Lauren J., Booth, Annie S., Gramacy, Robert B., Osthus, Dave
Format: Preprint
Published: 2024
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author Barnett, Steven D.
Beesley, Lauren J.
Booth, Annie S.
Gramacy, Robert B.
Osthus, Dave
author_facet Barnett, Steven D.
Beesley, Lauren J.
Booth, Annie S.
Gramacy, Robert B.
Osthus, Dave
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2408_01540
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Monotonic warpings for additive and deep Gaussian processes
Barnett, Steven D.
Beesley, Lauren J.
Booth, Annie S.
Gramacy, Robert B.
Osthus, Dave
Computation
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.
title Monotonic warpings for additive and deep Gaussian processes
topic Computation
url https://arxiv.org/abs/2408.01540