# Conformal prediction for full and sparse polynomial chaos expansions

arXiv: https://arxiv.org/abs/2601.16636 · HTML: https://mlsanity.com/paper/2601.16636/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 69 references that are in the map.
- First posted on arXiv 23 Jan 2026.

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

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Learning by Transduction](https://mlsanity.com/paper/1301.7375/) (2013)
- [A Conformal Prediction Approach to Explore Functional Data](https://mlsanity.com/paper/1302.6452/) (2013)
- [Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark](https://mlsanity.com/paper/2002.01290/) (2020)
- [Data-driven polynomial chaos expansion for machine learning regression](https://mlsanity.com/paper/1808.03216/) (2018)
- [Fast Exact Conformalization of Lasso using Piecewise Linear Homotopy](https://mlsanity.com/paper/1708.00427/) (2017)
- [An active-learning algorithm that combines sparse polynomial chaos expansions and bootstrap for structural reliability analysis](https://mlsanity.com/paper/1709.01589/) (2017)
- [Guaranteed Coverage Prediction Intervals with Gaussian Process Regression](https://mlsanity.com/paper/2310.15641/) (2023)
- [Automatic selection of basis-adaptive sparse polynomial chaos expansions for engineering applications](https://mlsanity.com/paper/2009.04800/) (2020)
- [Sparse Polynomial Chaos Expansions via Compressed Sensing and D-optimal Design](https://mlsanity.com/paper/1712.10131/) (2017)
- [Root-finding Approaches for Computing Conformal Prediction Set](https://mlsanity.com/paper/2104.06648/) (2021)
- [A spectral surrogate model for stochastic simulators computed from trajectory samples](https://mlsanity.com/paper/2207.05653/) (2022)
- [Sparse Polynomial Chaos expansions using Variational Relevance Vector Machines](https://mlsanity.com/paper/1912.11029/) (2019)

## Built on by (most cited first, 1 of 1)

- [AK-MCS-C2 : Active Kriging Monte Carlo Simulation method with conformal certification for failure probability estimation](https://mlsanity.com/paper/2606.20191/) (2026)

## Abstract (arXiv)

Polynomial Chaos Expansions (PCEs) are widely recognized for their efficient computational performance in surrogate modeling. Yet, a robust framework to quantify local model errors is still lacking. While the local uncertainty of PCE prediction can be captured using bootstrap resampling, other methods offering more rigorous statistical guarantees are needed, especially in the context of small training datasets. Recently, conformal predictions have demonstrated strong potential in machine learning, providing statistically robust and model-agnostic prediction intervals. Due to its generality and versatility, conformal prediction is especially valuable, as it can be adapted to suit a variety of problems, making it a compelling choice for PCE-based surrogate models. In this contribution, we explore its application to PCE-based surrogate models. More precisely, we present the integration of two conformal prediction methods, namely the full conformal and the Jackknife+ approaches, into both full and sparse PCEs. For full PCEs, we introduce computational shortcuts inspired by the inherent structure of regression methods to optimize the implementation of both conformal methods. For sparse PCEs, we incorporate the two approaches with appropriate modifications to the inference strategy, thereby circumventing the non-symmetrical nature of the regression algorithm and ensuring valid prediction intervals. Our developments yield better-calibrated prediction intervals for both full and sparse PCEs, achieving superior coverage over existing approaches, such as the bootstrap, while maintaining a moderate computational cost.