# Covariance-Boosted Gaussian Processes for Spatiotemporal Irregularities

arXiv: https://arxiv.org/abs/2607.23018 · HTML: https://mlsanity.com/paper/2607.23018/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 76 references that are in the map.
- First posted on arXiv 25 Jul 2026.

## Builds on (most cited first, 15 of 15)

- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [GPflow: A Gaussian process library using TensorFlow](https://mlsanity.com/paper/1610.08733/) (2016)
- [Input Warping for Bayesian Optimization of Non-stationary Functions](https://mlsanity.com/paper/1402.0929/) (2014)
- [Uniform Error Bounds for Gaussian Process Regression with Application to Safe Control](https://mlsanity.com/paper/1906.01376/) (2019)
- [Practical and Rigorous Uncertainty Bounds for Gaussian Process Regression](https://mlsanity.com/paper/2105.02796/) (2021)
- [Automatic Construction and Natural-Language Description of Nonparametric Regression Models](https://mlsanity.com/paper/1402.4304/) (2014)
- [Practical heteroskedastic Gaussian process modeling for large simulation experiments](https://mlsanity.com/paper/1611.05902/) (2016)
- [Non-Stationary Gaussian Process Regression with Hamiltonian Monte Carlo](https://mlsanity.com/paper/1508.04319/) (2015)
- [Gaussian Process Boosting](https://mlsanity.com/paper/2004.02653/) (2020)
- [Spatial Mapping with Gaussian Processes and Nonstationary Fourier Features](https://mlsanity.com/paper/1711.05615/) (2017)
- [Nonstationary Gaussian Process Surrogates](https://mlsanity.com/paper/2305.19242/) (2023)
- [A Unifying Perspective on Non-Stationary Kernels for Deeper Gaussian Processes](https://mlsanity.com/paper/2309.10068/) (2023)
- [Chained Gaussian Processes](https://mlsanity.com/paper/1604.05263/) (2016)
- [Mixtures of Gaussian Process Experts with SMC2](https://mlsanity.com/paper/2208.12830/) (2022)
- [Thin and Deep Gaussian Processes](https://mlsanity.com/paper/2310.11527/) (2023)

## Abstract (arXiv)

Nonstationary Gaussian process (GP) models are powerful tools for capturing input-dependent variability by adapting to observed data. However, with limited sampling and highly parameterized covariance structure, they are often prone to overfitting and overconfident uncertainty estimates, potentially leading to misleading predictions in safety-critical applications. Motivated by ionospheric modeling for satellite-based augmentation systems (SBAS), this paper proposes a Covariance-Boosted Gaussian Process (CBGP) framework centered upon boosting covariance priors to discover nonstationary latent functions for signal and observation variation that capture irregularities in the input domain. An additional layer of GP modeling of "partially-whitened" observations guides latent function relative error estimation that is used to iteratively update weak priors in a gradient descent-like procedure. Following boosting, restrictions are imposed upon prior covariances to prevent overfitting while posterior uncertainties are inflated to prevent model overconfidence. CBGP model efficacy and robustness are demonstrated through out-of-sample testing of both simulated and real-world applications that meet a three-nines integrity standard. The modeling of an extensive ionospheric storm dataset over South America suggests accurate and reliable means to compute SBAS ionospheric corrections in the most challenging space weather environment using regional models that are more informed and responsive than local fitting performed by currently-operating SBAS.