# From Conformal Predictions to Confidence Regions

arXiv: https://arxiv.org/abs/2405.18601 · HTML: https://mlsanity.com/paper/2405.18601/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 44 references that are in the map.
- First posted on arXiv 28 May 2024.

## Builds on (most cited first, 17 of 17)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [SelectiveNet: A Deep Neural Network with an Integrated Reject Option](https://mlsanity.com/paper/1901.09192/) (2019)
- [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
- [Distributional conformal prediction](https://mlsanity.com/paper/1909.07889/) (2019)
- [Universal Inference](https://mlsanity.com/paper/1912.11436/) (2019)
- [Conformal Bayesian Computation](https://mlsanity.com/paper/2106.06137/) (2021)
- [Regression with reject option and application to kNN](https://mlsanity.com/paper/2006.16597/) (2020)
- [Label Noise Robustness of Conformal Prediction](https://mlsanity.com/paper/2209.14295/) (2022)
- [Conformal Prediction via Regression-as-Classification](https://mlsanity.com/paper/2404.08168/) (2024)
- [MAPIE: an open-source library for distribution-free uncertainty quantification](https://mlsanity.com/paper/2207.12274/) (2022)
- [Sign-Perturbed Sums: A New System Identification Approach for Constructing Exact Non-Asymptotic Confidence Regions in Linear Regression Models](https://mlsanity.com/paper/1807.08216/) (2018)
- [Conformal Prediction Intervals with Temporal Dependence](https://mlsanity.com/paper/2205.12940/) (2022)
- [Distribution-Free Finite-Sample Guarantees and Split Conformal Prediction](https://mlsanity.com/paper/2210.14735/) (2022)
- [Finite Sample Confidence Regions for Linear Regression Parameters Using Arbitrary Predictors](https://mlsanity.com/paper/2401.15254/) (2024)

## Built on by (most cited first, 2 of 2)

- [Extending Prediction-Powered Inference through Conformal Prediction](https://mlsanity.com/paper/2510.16166/) (2025)
- [Robust Bayesian Optimization via Localized Online Conformal Prediction](https://mlsanity.com/paper/2411.17387/) (2024)

## Abstract (arXiv)

Conformal prediction methodologies have significantly advanced the quantification of uncertainties in predictive models. Yet, the construction of confidence regions for model parameters presents a notable challenge, often necessitating stringent assumptions regarding data distribution or merely providing asymptotic guarantees. We introduce a novel approach termed CCR, which employs a combination of conformal prediction intervals for the model outputs to establish confidence regions for model parameters. We present coverage guarantees under minimal assumptions on noise and that is valid in finite sample regime. Our approach is applicable to both split conformal predictions and black-box methodologies including full or cross-conformal approaches. In the specific case of linear models, the derived confidence region manifests as the feasible set of a Mixed-Integer Linear Program (MILP), facilitating the deduction of confidence intervals for individual parameters and enabling robust optimization. We empirically compare CCR to recent advancements in challenging settings such as with heteroskedastic and non-Gaussian noise.