# Guaranteed Coverage Prediction Intervals with Gaussian Process Regression

arXiv: https://arxiv.org/abs/2310.15641 · HTML: https://mlsanity.com/paper/2310.15641/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 56 references that are in the map.
- First posted on arXiv 24 Oct 2023.

## Builds on (most cited first, 19 of 19)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Learning to Drive in a Day](https://mlsanity.com/paper/1807.00412/) (2018)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Learning by Transduction](https://mlsanity.com/paper/1301.7375/) (2013)
- [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)
- [Regression Conformal Prediction with Nearest Neighbours](https://mlsanity.com/paper/1401.3880/) (2014)
- [Practical and Rigorous Uncertainty Bounds for Gaussian Process Regression](https://mlsanity.com/paper/2105.02796/) (2021)
- [Fast Exact Conformalization of Lasso using Piecewise Linear Homotopy](https://mlsanity.com/paper/1708.00427/) (2017)
- [Computationally efficient versions of conformal predictive distributions](https://mlsanity.com/paper/1911.00941/) (2019)
- [Conformal Prediction Interval Estimations with an Application to Day-Ahead and Intraday Power Markets](https://mlsanity.com/paper/1905.07886/) (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)
- [Scalable Joint Models for Reliable Uncertainty-Aware Event Prediction](https://mlsanity.com/paper/1708.04757/) (2017)
- [Efficient Optimization for Sparse Gaussian Process Regression](https://mlsanity.com/paper/1310.6007/) (2013)
- [A Cross-Conformal Predictor for Multi-label Classification](https://mlsanity.com/paper/2211.16238/) (2022)

## Built on by (most cited first, 12 of 12)

- [Uncertainty quantification for probabilistic machine learning in earth observation using conformal prediction](https://mlsanity.com/paper/2401.06421/) (2024)
- [TorchCP: A Python Library for Conformal Prediction](https://mlsanity.com/paper/2402.12683/) (2024)
- [Conformal Approach To Gaussian Process Surrogate Evaluation With Coverage Guarantees](https://mlsanity.com/paper/2401.07733/) (2024)
- [Uncertainty quantification in automated valuation models with spatially weighted conformal prediction](https://mlsanity.com/paper/2312.06531/) (2023)
- [Gaussian process interpolation with conformal prediction: methods and comparative analysis](https://mlsanity.com/paper/2407.08271/) (2024)
- [Online scalable Gaussian processes with conformal prediction for guaranteed coverage](https://mlsanity.com/paper/2410.05444/) (2024)
- [Uncertainty Estimation for Path Loss and Radio Metric Models](https://mlsanity.com/paper/2501.06308/) (2025)
- [Scalable and adaptive prediction bands with kernel sum-of-squares](https://mlsanity.com/paper/2505.21039/) (2025)
- [Approximating Full Conformal Prediction for Neural Network Regression with Gauss-Newton Influence](https://mlsanity.com/paper/2507.20272/) (2025)
- [Conformal prediction for full and sparse polynomial chaos expansions](https://mlsanity.com/paper/2601.16636/) (2026)
- [Inductive Conformal Prediction under Data Scarcity: Exploring the Impacts of Nonconformity Measures](https://mlsanity.com/paper/2410.09894/) (2024)
- [Tackling Incomplete Data in Air Quality Prediction: A Bayesian Deep Learning Framework for Uncertainty Quantification](https://mlsanity.com/paper/2511.02175/) (2025)

## Abstract (arXiv)

Gaussian Process Regression (GPR) is a popular regression method, which unlike most Machine Learning techniques, provides estimates of uncertainty for its predictions. These uncertainty estimates however, are based on the assumption that the model is well-specified, an assumption that is violated in most practical applications, since the required knowledge is rarely available. As a result, the produced uncertainty estimates can become very misleading; for example the prediction intervals (PIs) produced for the 95% confidence level may cover much less than 95% of the true labels. To address this issue, this paper introduces an extension of GPR based on a Machine Learning framework called, Conformal Prediction (CP). This extension guarantees the production of PIs with the required coverage even when the model is completely misspecified. The proposed approach combines the advantages of GPR with the valid coverage guarantee of CP, while the performed experimental results demonstrate its superiority over existing methods.