# Compactly-supported nonstationary kernels for computing exact Gaussian processes on big data

arXiv: https://arxiv.org/abs/2411.05869 · HTML: https://mlsanity.com/paper/2411.05869/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 72 references that are in the map.
- First posted on arXiv 7 Nov 2024.

## Builds on (most cited first, 14 of 14)

- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)](https://mlsanity.com/paper/1503.01057/) (2015)
- [Exact Gaussian Processes on a Million Data Points](https://mlsanity.com/paper/1903.08114/) (2019)
- [Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets](https://mlsanity.com/paper/1406.7343/) (2014)
- [A general framework for Vecchia approximations of Gaussian processes](https://mlsanity.com/paper/1708.06302/) (2017)
- [A Case Study Competition Among Methods for Analyzing Large Spatial Data](https://mlsanity.com/paper/1710.05013/) (2017)
- [Exact Gaussian Processes for Massive Datasets via Non-Stationary Sparsity-Discovering Kernels](https://mlsanity.com/paper/2205.09070/) (2022)
- [A Unifying Perspective on Non-Stationary Kernels for Deeper Gaussian Processes](https://mlsanity.com/paper/2309.10068/) (2023)
- [Uncertainty Quantification for Bayesian Optimization](https://mlsanity.com/paper/2002.01569/) (2020)
- [Sharded Bayesian Additive Regression Trees](https://mlsanity.com/paper/2306.00361/) (2023)
- [Regression-based covariance functions for nonstationary spatial modeling](https://mlsanity.com/paper/1410.1494/) (2014)
- [Hybrid Parameter Search and Dynamic Model Selection for Mixed-Variable Bayesian Optimization](https://mlsanity.com/paper/2206.01409/) (2022)
- [Mixed-Stationary Gaussian Process for Flexible Non-Stationary Modeling of Spatial Outcomes](https://mlsanity.com/paper/1807.06656/) (2018)
- [Vecchia Gaussian Processes: on probabilistic and statistical properties](https://mlsanity.com/paper/2410.10649/) (2024)

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

- [GGMPs: Generalized Gaussian Mixture Processes](https://mlsanity.com/paper/2603.10442/) (2026)
- [Compactly supported radial basis functions as probability density functions](https://mlsanity.com/paper/2607.26759/) (2026)

## Abstract (arXiv)

The Gaussian process (GP) is a widely used probabilistic machine learning method with implicit uncertainty characterization for stochastic function approximation, stochastic modeling, and analyzing real-world measurements of nonlinear processes. Traditional implementations of GPs involve stationary kernels (also termed covariance functions) that limit their flexibility, and exact methods for inference that prevent application to data sets with more than about ten thousand points. Modern approaches to address stationarity assumptions generally fail to accommodate large data sets, while all attempts to address scalability focus on approximating the Gaussian likelihood, which can involve subjectivity and lead to inaccuracies. In this work, we explicitly derive an alternative kernel that can discover and encode both sparsity and nonstationarity. We embed the kernel within a fully Bayesian GP model and leverage high-performance computing resources to enable the analysis of massive data sets. We demonstrate the favorable performance of our novel kernel relative to existing exact and approximate GP methods across a variety of synthetic data examples. Furthermore, we conduct space-time prediction based on more than one million measurements of daily maximum temperature and verify that our results outperform state-of-the-art methods in the Earth sciences. More broadly, having access to exact GPs that use ultra-scalable, sparsity-discovering, nonstationary kernels allows GP methods to truly compete with a wide variety of machine learning methods.