# Conformal Approach To Gaussian Process Surrogate Evaluation With Coverage Guarantees

arXiv: https://arxiv.org/abs/2401.07733 · HTML: https://mlsanity.com/paper/2401.07733/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 46 references that are in the map.
- First posted on arXiv 15 Jan 2024.

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

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantification](https://mlsanity.com/paper/1802.00850/) (2018)
- [Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review](https://mlsanity.com/paper/2303.10462/) (2023)
- [Regression Conformal Prediction with Nearest Neighbours](https://mlsanity.com/paper/1401.3880/) (2014)
- [Bayesian Optimization with Conformal Prediction Sets](https://mlsanity.com/paper/2210.12496/) (2022)
- [Fast Exact Conformalization of Lasso using Piecewise Linear Homotopy](https://mlsanity.com/paper/1708.00427/) (2017)
- [Valid model-free spatial prediction](https://mlsanity.com/paper/2006.15640/) (2020)
- [Improving Adaptive Conformal Prediction Using Self-Supervised Learning](https://mlsanity.com/paper/2302.12238/) (2023)
- [Efficiency of conformalized ridge regression](https://mlsanity.com/paper/1404.2083/) (2014)
- [Guaranteed Coverage Prediction Intervals with Gaussian Process Regression](https://mlsanity.com/paper/2310.15641/) (2023)
- [Adaptive Conformal Regression with Jackknife+ Rescaled Scores](https://mlsanity.com/paper/2305.19901/) (2023)
- [Conformalized Kernel Ridge Regression](https://mlsanity.com/paper/1609.05959/) (2016)
- [A comparison between Bayesian and ordinary kriging based on validation criteria: application to radiological characterisation](https://mlsanity.com/paper/2305.07314/) (2023)

## Built on by (most cited first, 7 of 7)

- [Epistemic Uncertainty in Conformal Scores: A Unified Approach](https://mlsanity.com/paper/2502.06995/) (2025)
- [Gaussian process interpolation with conformal prediction: methods and comparative analysis](https://mlsanity.com/paper/2407.08271/) (2024)
- [Learning signals defined on graphs with optimal transport and Gaussian process regression](https://mlsanity.com/paper/2410.15721/) (2024)
- [Conformalised Conditional Normalising Flows for Joint Prediction Regions in time series](https://mlsanity.com/paper/2411.17042/) (2024)
- [Scalable and adaptive prediction bands with kernel sum-of-squares](https://mlsanity.com/paper/2505.21039/) (2025)
- [Gaussian process surrogate model to approximate power grid simulators -- An application to the certification of a congestion management controller](https://mlsanity.com/paper/2503.00094/) (2025)
- [CREDO: Epistemic-Aware Conformalized Credal Envelopes for Regression](https://mlsanity.com/paper/2603.06826/) (2026)

## Abstract (arXiv)

Gaussian processes (GPs) are a Bayesian machine learning approach widely used to construct surrogate models for the uncertainty quantification of computer simulation codes in industrial applications. It provides both a mean predictor and an estimate of the posterior prediction variance, the latter being used to produce Bayesian credibility intervals. Interpreting these intervals relies on the Gaussianity of the simulation model as well as the well-specification of the priors which are not always appropriate. We propose to address this issue with the help of conformal prediction. In the present work, a method for building adaptive cross-conformal prediction intervals is proposed by weighting the non-conformity score with the posterior standard deviation of the GP. The resulting conformal prediction intervals exhibit a level of adaptivity akin to Bayesian credibility sets and display a significant correlation with the surrogate model local approximation error, while being free from the underlying model assumptions and having frequentist coverage guarantees. These estimators can thus be used for evaluating the quality of a GP surrogate model and can assist a decision-maker in the choice of the best prior for the specific application of the GP. The performance of the method is illustrated through a panel of numerical examples based on various reference databases. Moreover, the potential applicability of the method is demonstrated in the context of surrogate modeling of an expensive-to-evaluate simulator of the clogging phenomenon in steam generators of nuclear reactors.