Monotonic warpings for additive and deep Gaussian processes

TL;DR

This paper introduces a novel monotonic Gaussian process construction that efficiently models constrained responses, extending to multiple inputs and deep Gaussian processes, with demonstrated improved performance on benchmark problems.

Contribution

The paper presents a new monotonic Gaussian process method using transformations and elliptical slice sampling, applicable to single and multiple inputs, and integrated into deep Gaussian processes.

Findings

Improved accuracy over state-of-the-art methods on benchmark problems.

Efficient monotonic Gaussian process construction for single input.

Effective deployment in additive and deep Gaussian process models.

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.