# Mind the Jumps: A Scalable Robust Local Gaussian Process for Multidimensional Response Surfaces with Discontinuities

arXiv: https://arxiv.org/abs/2512.12574 · HTML: https://mlsanity.com/paper/2512.12574/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 63 references that are in the map.
- First posted on arXiv 14 Dec 2025.

## Builds on (most cited first, 11 of 11)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [Local Gaussian process approximation for large computer experiments](https://mlsanity.com/paper/1303.0383/) (2013)
- [Active Learning for Deep Gaussian Process Surrogates](https://mlsanity.com/paper/2012.08015/) (2020)
- [Non-Stationary Gaussian Process Regression with Hamiltonian Monte Carlo](https://mlsanity.com/paper/1508.04319/) (2015)
- [Non-Stationary Spatial Modeling](https://mlsanity.com/paper/2212.08043/) (2022)
- [Locally induced Gaussian processes for large-scale simulation experiments](https://mlsanity.com/paper/2008.12857/) (2020)
- [Gaining Outlier Resistance with Progressive Quantiles: Fast Algorithms and Theoretical Studies](https://mlsanity.com/paper/2112.08471/) (2021)
- [Scaled Gaussian Stochastic Process for Computer Model Calibration and Prediction](https://mlsanity.com/paper/1707.08215/) (2017)
- [Slow Kill for Big Data Learning](https://mlsanity.com/paper/2305.01726/) (2023)

## Built on by (most cited first, 1 of 1)

- [Adaptive multi-resolution Gaussian processes: Scalable exact inference with naturally data-sparse covariance matrices](https://mlsanity.com/paper/2609.30348/) (2026)

## Abstract (arXiv)

Modeling response surfaces with abrupt jumps and discontinuities remains a major challenge across scientific and engineering domains. Although Gaussian process models excel at capturing smooth nonlinear relationships, their stationarity assumptions limit their ability to adapt to sudden input-output variations. Existing nonstationary extensions, particularly those based on domain partitioning, often struggle with boundary inconsistencies, sensitivity to outliers, and scalability issues in higher-dimensional settings, leading to reduced predictive accuracy and unreliable parameter estimation. To address these challenges, this paper proposes the Robust Local Gaussian Process (RLGP) model, a framework that integrates adaptive nearest-neighbor selection with a sparsity-driven robustification mechanism. Unlike existing methods, RLGP leverages an optimization-based mean-shift adjustment after a multivariate perspective transformation combined with local neighborhood modeling to mitigate the influence of outliers. This approach improves predictive accuracy near discontinuities while enhancing robustness to data heterogeneity. Comprehensive evaluations on real-world datasets show that RLGP consistently delivers high predictive accuracy and maintains competitive computational efficiency, especially in scenarios with sharp transitions and complex response structures. Scalability tests further confirm RLGP's stability and reliability in higher-dimensional settings, where other methods struggle. These results establish RLGP as an effective and practical solution for modeling nonstationary and discontinuous response surfaces across a wide range of applications.