# Modular Jump Gaussian Processes

arXiv: https://arxiv.org/abs/2505.15557 · HTML: https://mlsanity.com/paper/2505.15557/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 59 references that are in the map.
- First posted on arXiv 21 May 2025.

## Builds on (most cited first, 10 of 10)

- [Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets](https://mlsanity.com/paper/1406.7343/) (2014)
- [Local Gaussian process approximation for large computer experiments](https://mlsanity.com/paper/1303.0383/) (2013)
- [Locally induced Gaussian processes for large-scale simulation experiments](https://mlsanity.com/paper/2008.12857/) (2020)
- [Nonstationary Gaussian Process Surrogates](https://mlsanity.com/paper/2305.19242/) (2023)
- [Ordinal Bayesian Optimisation](https://mlsanity.com/paper/1912.02493/) (2019)
- [Sequential Adaptive Design for Jump Regression Estimation](https://mlsanity.com/paper/1904.01648/) (2019)
- [Active Learning of Piecewise Gaussian Process Surrogates](https://mlsanity.com/paper/2301.08789/) (2023)
- [Massively parallel approximate Gaussian process regression](https://mlsanity.com/paper/1310.5182/) (2013)
- [A Conditional Density Estimation Partition Model Using Logistic Gaussian Processes](https://mlsanity.com/paper/1703.06978/) (2017)
- [Speeding up neighborhood search in local Gaussian process prediction](https://mlsanity.com/paper/1409.0074/) (2014)

## Built on by (most cited first, 2 of 2)

- [All Emulators are Wrong, Many are Useful, and Some are More Useful Than Others: A Reproducible Comparison of Computer Model Surrogates](https://mlsanity.com/paper/2512.09060/) (2025)
- [Generative Bayesian Computation as a Scalable Alternative to Gaussian Process Surrogates](https://mlsanity.com/paper/2602.21408/) (2026)

## Abstract (arXiv)

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.