# Sharp Calibrated Gaussian Processes

arXiv: https://arxiv.org/abs/2302.11961 · HTML: https://mlsanity.com/paper/2302.11961/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 29 references that are in the map.
- First posted on arXiv 23 Feb 2023.

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

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Concrete Dropout](https://mlsanity.com/paper/1705.07832/) (2017)
- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [Gaussian Processes for Data-Efficient Learning in Robotics and Control](https://mlsanity.com/paper/1502.02860/) (2015)
- [Distribution Calibration for Regression](https://mlsanity.com/paper/1905.06023/) (2019)
- [Bayesian Model Selection, the Marginal Likelihood, and Generalization](https://mlsanity.com/paper/2202.11678/) (2022)
- [No-Regret Bayesian Optimization with Unknown Hyperparameters](https://mlsanity.com/paper/1901.03357/) (2019)
- [On the marginal likelihood and cross-validation](https://mlsanity.com/paper/1905.08737/) (2019)
- [Calibrated and Sharp Uncertainties in Deep Learning via Density Estimation](https://mlsanity.com/paper/2112.07184/) (2021)
- [Conformal calibrators](https://mlsanity.com/paper/1902.06579/) (2019)
- [Gaussian Process Uniform Error Bounds with Unknown Hyperparameters for Safety-Critical Applications](https://mlsanity.com/paper/2109.02606/) (2021)
- [Modular Conformal Calibration](https://mlsanity.com/paper/2206.11468/) (2022)

## Built on by (most cited first, 5 of 5)

- [Multi-fidelity Gaussian process surrogate modeling for regression problems in physics](https://mlsanity.com/paper/2404.11965/) (2024)
- [Interventional Processes for Causal Uncertainty Quantification](https://mlsanity.com/paper/2410.14483/) (2024)
- [Wiener Chaos in Kernel Regression: Towards Untangling Aleatoric and Epistemic Uncertainty](https://mlsanity.com/paper/2312.07387/) (2023)
- [A Decision-driven Methodology for Designing Uncertainty-aware AI Self-Assessment](https://mlsanity.com/paper/2408.01301/) (2024)
- [Online Sharp-Calibrated Bayesian Optimization](https://mlsanity.com/paper/2605.10572/) (2026)

## Abstract (arXiv)

While Gaussian processes are a mainstay for various engineering and scientific applications, the uncertainty estimates don't satisfy frequentist guarantees and can be miscalibrated in practice. State-of-the-art approaches for designing calibrated models rely on inflating the Gaussian process posterior variance, which yields confidence intervals that are potentially too coarse. To remedy this, we present a calibration approach that generates predictive quantiles using a computation inspired by the vanilla Gaussian process posterior variance but using a different set of hyperparameters chosen to satisfy an empirical calibration constraint. This results in a calibration approach that is considerably more flexible than existing approaches, which we optimize to yield tight predictive quantiles. Our approach is shown to yield a calibrated model under reasonable assumptions. Furthermore, it outperforms existing approaches in sharpness when employed for calibrated regression.