# Selecting informative conformal prediction sets with false coverage rate control

arXiv: https://arxiv.org/abs/2403.12295 · HTML: https://mlsanity.com/paper/2403.12295/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 44 references that are in the map.
- First posted on arXiv 18 Mar 2024.

## Builds on (most cited first, 22 of 22)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Testing for Outliers with Conformal p-values](https://mlsanity.com/paper/2104.08279/) (2021)
- [Class-Conditional Conformal Prediction with Many Classes](https://mlsanity.com/paper/2306.09335/) (2023)
- [Nested conformal prediction and quantile out-of-bag ensemble methods](https://mlsanity.com/paper/1910.10562/) (2019)
- [A Conformal Prediction Approach to Explore Functional Data](https://mlsanity.com/paper/1302.6452/) (2013)
- [Conformal Prediction using Conditional Histograms](https://mlsanity.com/paper/2105.08747/) (2021)
- [Selection by Prediction with Conformal p-values](https://mlsanity.com/paper/2210.01408/) (2022)
- [Transductive conformal inference with adaptive scores](https://mlsanity.com/paper/2310.18108/) (2023)
- [Adaptive novelty detection with false discovery rate guarantee](https://mlsanity.com/paper/2208.06685/) (2022)
- [Confidence on the Focal: Conformal Prediction with Selection-Conditional Coverage](https://mlsanity.com/paper/2403.03868/) (2024)
- [Online Control of the False Coverage Rate and False Sign Rate](https://mlsanity.com/paper/1905.01059/) (2019)
- [Selective conformal inference with false coverage-statement rate control](https://mlsanity.com/paper/2301.00584/) (2023)
- [A unified treatment of multiple testing with prior knowledge using the p-filter](https://mlsanity.com/paper/1703.06222/) (2017)
- [A Burden Shared is a Burden Halved: A Fairness-Adjusted Approach to Classification](https://mlsanity.com/paper/2110.05720/) (2021)
- [Error rate control for classification rules in multiclass mixture models](https://mlsanity.com/paper/2109.14235/) (2021)
- [Selective Sign-Determining Multiple Confidence Intervals with FCR Control](https://mlsanity.com/paper/1404.7403/) (2014)
- [On Stepwise Control of Directional Errors under Independence and Some Dependence](https://mlsanity.com/paper/1602.02854/) (2016)
- [A constructive approach to selective risk control](https://mlsanity.com/paper/2401.16651/) (2024)

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

- [Selective Conformal Risk Control](https://mlsanity.com/paper/2512.12844/) (2025)
- [Powerful batch conformal prediction for classification](https://mlsanity.com/paper/2411.02239/) (2024)
- [Model-agnostic Selective Labeling with Provable Statistical Guarantees](https://mlsanity.com/paper/2510.14581/) (2025)
- [Conformal Risk-Averse Decision Making with Action Conditional Guarantee](https://mlsanity.com/paper/2606.05551/) (2026)
- [Elements of Conformal Prediction](https://mlsanity.com/paper/2603.23923/) (2026)
- [Online Selective Conformal Prediction with Asymmetric Rules: A Permutation Test Approach](https://mlsanity.com/paper/2602.10018/) (2026)
- [Neyman-Pearson Classification with Indecisions: Simultaneous Control of Selective Type I and Type II Errors](https://mlsanity.com/paper/2610.04233/) (2026)

## Abstract (arXiv)

In supervised learning, including regression and classification, conformal methods provide prediction sets for the outcome/label with finite sample coverage for any machine learning predictor. We consider here the case where such prediction sets come after a selection process. The selection process requires that the selected prediction sets be `informative' in a well defined sense. We consider both the classification and regression settings where the analyst may consider as informative only the sample with prediction sets small enough, excluding null values, or obeying other appropriate `monotone' constraints. We develop a unified framework for building such informative conformal prediction sets while controlling the false coverage rate (FCR) on the selected sample. While conformal prediction sets after selection have been the focus of much recent literature in the field, the new introduced procedures, called InfoSP and InfoSCOP, are to our knowledge the first ones providing FCR control for informative prediction sets. We show the usefulness of our resulting procedures on real and simulated data.