# Optimized conformal classification using gradient descent approximation

arXiv: https://arxiv.org/abs/2105.11255 · HTML: https://mlsanity.com/paper/2105.11255/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 11 references that are in the map.
- First posted on arXiv 24 May 2021.

## Builds on (most cited first, 3 of 3)

- [High-Quality Prediction Intervals for Deep Learning: A Distribution-Free, Ensembled Approach](https://mlsanity.com/paper/1802.07167/) (2018)
- [Criteria of efficiency for conformal prediction](https://mlsanity.com/paper/1603.04416/) (2016)
- [Training conformal predictors](https://mlsanity.com/paper/2005.07037/) (2020)

## Built on by (most cited first, 28 of 28)

- [Learning Optimal Conformal Classifiers](https://mlsanity.com/paper/2110.09192/) (2021)
- [Training Uncertainty-Aware Classifiers with Conformalized Deep Learning](https://mlsanity.com/paper/2205.05878/) (2022)
- [Conformal Prediction for Deep Classifier via Label Ranking](https://mlsanity.com/paper/2310.06430/) (2023)
- [On the Utility of Prediction Sets in Human-AI Teams](https://mlsanity.com/paper/2205.01411/) (2022)
- [An Information Theoretic Perspective on Conformal Prediction](https://mlsanity.com/paper/2405.02140/) (2024)
- [Conformal inference is (almost) free for neural networks trained with early stopping](https://mlsanity.com/paper/2301.11556/) (2023)
- [On the Expected Size of Conformal Prediction Sets](https://mlsanity.com/paper/2306.07254/) (2023)
- [Conformal Risk Minimization with Variance Reduction](https://mlsanity.com/paper/2411.01696/) (2024)
- [TorchCP: A Python Library for Conformal Prediction](https://mlsanity.com/paper/2402.12683/) (2024)
- [Direct Prediction Set Minimization via Bilevel Conformal Classifier Training](https://mlsanity.com/paper/2506.06599/) (2025)
- [C-Adapter: Adapting Deep Classifiers for Efficient Conformal Prediction Sets](https://mlsanity.com/paper/2410.09408/) (2024)
- [Enhancing Trustworthiness of Graph Neural Networks with Rank-Based Conformal Training](https://mlsanity.com/paper/2501.02767/) (2025)
- [Reliable Prediction Intervals with Directly Optimized Inductive Conformal Regression for Deep Learning](https://mlsanity.com/paper/2302.00872/) (2023)
- [Non-exchangeable Conformal Prediction with Optimal Transport: Tackling Distribution Shifts with Unlabeled Data](https://mlsanity.com/paper/2507.10425/) (2025)
- [Test-time augmentation improves efficiency in conformal prediction](https://mlsanity.com/paper/2505.22764/) (2025)
- [Bayesian Conformal Prediction as a Decision Risk Problem](https://mlsanity.com/paper/2602.03331/) (2026)
- [Elements of Conformal Prediction](https://mlsanity.com/paper/2603.23923/) (2026)
- [Audited Conformal Prediction for Classification under Unknown Distribution Shift](https://mlsanity.com/paper/2606.14909/) (2026)
- [Investigating Data Usage for Inductive Conformal Predictors](https://mlsanity.com/paper/2406.12262/) (2024)
- [Adjusting Regression Models for Conditional Uncertainty Calibration](https://mlsanity.com/paper/2409.17466/) (2024)
- [CoFineLLM: Conformal Finetuning of LLMs for Language-Instructed Robot Planning](https://mlsanity.com/paper/2511.06575/) (2025)
- [Cost-Sensitive Conformal Training with Provably Controllable Learning Bounds](https://mlsanity.com/paper/2511.17861/) (2025)
- [Class Adaptive Conformal Training](https://mlsanity.com/paper/2601.09522/) (2026)
- [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)
- [Decoupled Conformal Optimisation: Efficient Prediction Sets via Independent Tuning and Calibration](https://mlsanity.com/paper/2605.18354/) (2026)
- [SPACR: Single-Pass Adaptive Training of Uncertainty-Aware Conformal Regressors](https://mlsanity.com/paper/2606.10734/) (2026)
- [Conformal Risk Minimization for Semi-Supervised Domain Adaptation via Optimal Transport](https://mlsanity.com/paper/2608.23153/) (2026)

## Abstract (arXiv)

Conformal predictors are an important class of algorithms that allow predictions to be made with a user-defined confidence level. They are able to do this by outputting prediction sets, rather than simple point predictions. The conformal predictor is valid in the sense that the accuracy of its predictions is guaranteed to meet the confidence level, only assuming exchangeability in the data. Since accuracy is guaranteed, the performance of a conformal predictor is measured through the efficiency of the prediction sets. Typically, a conformal predictor is built on an underlying machine learning algorithm and hence its predictive power is inherited from this algorithm. However, since the underlying machine learning algorithm is not trained with the objective of minimizing predictive efficiency it means that the resulting conformal predictor may be sub-optimal and not aligned sufficiently to this objective. Hence, in this study we consider an approach to train the conformal predictor directly with maximum predictive efficiency as the optimization objective, and we focus specifically on the inductive conformal predictor for classification. To do this, the conformal predictor is approximated by a differentiable objective function and gradient descent used to optimize it. The resulting parameter estimates are then passed to a proper inductive conformal predictor to give valid prediction sets. We test the method on several real world data sets and find that the method is promising and in most cases gives improved predictive efficiency against a baseline conformal predictor.