SILO: 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.

Bio

Robert is a Professor of Statistics, and Head of the Department of Statistics in the College of Science at Virginia Polytechnic and State University. He has received a Ph.D. in Applied Mathematics & Statistics, University of California, Santa Cruz, December 2005 and M.Sc. Computer Science, University of California, Santa Cruz, April 2003.