Modular Jump Gaussian Processes

Gaussian processes (GPs) furnish accurate nonlinear predictions with well-calibrated uncertainty. However, the typical GP setup has a built-in stationarity assumption, making it ill-suited for modeling data from processes with sudden changes, or "jumps" in the output variable. The "jump GP" (JGP) was developed for modeling data from such processes, combining local GPs and latent "level" variables under a joint inferential framework. But joint modeling can be fraught with difficulty. We aim to simplify by suggesting a more modular setup, eschewing joint inference but retaining the main JGP themes: (a) learning optimal neighborhood sizes that locally respect manifolds of discontinuity; and (b) a new cluster-based (latent) feature to capture regions of distinct output levels on both sides of the manifold. We show that each of (a) and (b) separately leads to dramatic improvements when modeling processes with jumps. In tandem (but without requiring joint inference) that benefit is compounded, as illustrated on real and synthetic benchmark examples from the recent literature.