# Training conformal predictors

arXiv: https://arxiv.org/abs/2005.07037 · HTML: https://mlsanity.com/paper/2005.07037/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 May 2020.

## Built on by (most cited first, 20 of 20)

- [Training Uncertainty-Aware Classifiers with Conformalized Deep Learning](https://mlsanity.com/paper/2205.05878/) (2022)
- [Copula-based conformal prediction for Multi-Target Regression](https://mlsanity.com/paper/2101.12002/) (2021)
- [Conformal Prediction for Deep Classifier via Label Ranking](https://mlsanity.com/paper/2310.06430/) (2023)
- [Optimized conformal classification using gradient descent approximation](https://mlsanity.com/paper/2105.11255/) (2021)
- [An Information Theoretic Perspective on Conformal Prediction](https://mlsanity.com/paper/2405.02140/) (2024)
- [Integrative conformal p-values for powerful out-of-distribution testing with labeled outliers](https://mlsanity.com/paper/2208.11111/) (2022)
- [Conformal inference is (almost) free for neural networks trained with early stopping](https://mlsanity.com/paper/2301.11556/) (2023)
- [Does confidence calibration improve conformal prediction?](https://mlsanity.com/paper/2402.04344/) (2024)
- [Normalizing Flows for Conformal Regression](https://mlsanity.com/paper/2406.03346/) (2024)
- [Conformal Risk Minimization with Variance Reduction](https://mlsanity.com/paper/2411.01696/) (2024)
- [Game-Theoretic Defenses for Robust Conformal Prediction Against Adversarial Attacks in Medical Imaging](https://mlsanity.com/paper/2411.04376/) (2024)
- [Conformal Policy Control](https://mlsanity.com/paper/2603.02196/) (2026)
- [Approximation to Object Conditional Validity with Inductive Conformal Predictors](https://mlsanity.com/paper/2102.07436/) (2021)
- [Elements of Conformal Prediction](https://mlsanity.com/paper/2603.23923/) (2026)
- [Adjusting Regression Models for Conditional Uncertainty Calibration](https://mlsanity.com/paper/2409.17466/) (2024)
- [Assumption-free fidelity bounds for hardware noise characterization](https://mlsanity.com/paper/2504.07010/) (2025)
- [CoFineLLM: Conformal Finetuning of LLMs for Language-Instructed Robot Planning](https://mlsanity.com/paper/2511.06575/) (2025)
- [Softmax is not Enough (for Adaptive Conformal Classification)](https://mlsanity.com/paper/2602.19498/) (2026)
- [ConformalHDC: Uncertainty-Aware Hyperdimensional Computing with Application to Neural Decoding](https://mlsanity.com/paper/2602.21446/) (2026)
- [SPACR: Single-Pass Adaptive Training of Uncertainty-Aware Conformal Regressors](https://mlsanity.com/paper/2606.10734/) (2026)

## Abstract (arXiv)

Efficiency criteria for conformal prediction, such as observed fuzziness (i.e., the sum of p-values associated with false labels), are commonly used to evaluate the performance of given conformal predictors. Here, we investigate whether it is possible to exploit efficiency criteria to learn classifiers, both conformal predictors and point classifiers, by using such criteria as training objective functions. The proposed idea is implemented for the problem of binary classification of hand-written digits. By choosing a 1-dimensional model class (with one real-valued free parameter), we can solve the optimization problems through an (approximate) exhaustive search over (a discrete version of) the parameter space. Our empirical results suggest that conformal predictors trained by minimizing their observed fuzziness perform better than conformal predictors trained in the traditional way by minimizing the prediction error of the corresponding point classifier. They also have a reasonable performance in terms of their prediction error on the test set.