GP+: A Python library for kernel-based learning via Gaussian processes

Abstract

In this paper we introduce GP+, an open-source library for kernel-based learning via Gaussian processes (GPs) which are powerful statistical models that are completely characterized by their parametric covariance and mean functions. GP+ is built on PyTorch and provides a user-friendly and object-oriented tool for probabilistic learning and inference. As we demonstrate with a host of examples, GP+ has a few unique advantages over other GP modeling libraries. We achieve these advantages primarily by integrating nonlinear manifold learning techniques with GPs’ covariance and mean functions. As part of introducing GP+, in this paper we also make methodological contributions that $\left(1\right)$ enable probabilistic data fusion and inverse parameter estimation, and $\left(2\right)$ equip GPs with parsimonious parametric mean functions which span mixed feature spaces that have both categorical and quantitative variables. We demonstrate the impact of these contributions in the context of Bayesian optimization, multi-fidelity modeling, sensitivity analysis, and calibration of computer models.