# Selective Conformal Risk Control

arXiv: https://arxiv.org/abs/2512.12844 · HTML: https://mlsanity.com/paper/2512.12844/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 31 references that are in the map.
- First posted on arXiv 14 Dec 2025.

## Builds on (most cited first, 23 of 23)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [SelectiveNet: A Deep Neural Network with an Integrated Reject Option](https://mlsanity.com/paper/1901.09192/) (2019)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Evaluating model calibration in classification](https://mlsanity.com/paper/1902.06977/) (2019)
- [Machine Learning with a Reject Option: A survey](https://mlsanity.com/paper/2107.11277/) (2021)
- [Optimal strategies for reject option classifiers](https://mlsanity.com/paper/2101.12523/) (2021)
- [Calibrated Selective Classification](https://mlsanity.com/paper/2208.12084/) (2022)
- [Conformal Prediction Sets with Limited False Positives](https://mlsanity.com/paper/2202.07650/) (2022)
- [AUC-based Selective Classification](https://mlsanity.com/paper/2210.10703/) (2022)
- [Selective conformal inference with false coverage-statement rate control](https://mlsanity.com/paper/2301.00584/) (2023)
- [Conformal Risk Control for Ordinal Classification](https://mlsanity.com/paper/2405.00417/) (2024)
- [Selecting informative conformal prediction sets with false coverage rate control](https://mlsanity.com/paper/2403.12295/) (2024)
- [Two-stage Risk Control with Application to Ranked Retrieval](https://mlsanity.com/paper/2404.17769/) (2024)

## Built on by (most cited first, 11 of 11)

- [Proof-Carrying Agent Actions: Model-Agnostic Runtime Governance for Heterogeneous Agent Systems](https://mlsanity.com/paper/2606.04104/) (2026)
- [A Joint Finite-Sample Certificate for Adaptive Selective Conformal Risk Control](https://mlsanity.com/paper/2606.08517/) (2026)
- [When Can Conformal Risk Control Certify LLM Outputs? Bounds, Impossibility, and Adaptation for Structured Generation](https://mlsanity.com/paper/2606.29054/) (2026)
- [Improving Backward Conformal Prediction via Non-Conformity Score Transformation](https://mlsanity.com/paper/2602.01733/) (2026)
- [Weighted Bayesian Conformal Prediction](https://mlsanity.com/paper/2604.06464/) (2026)
- [Explainable Wastewater Digital Twins: Adaptive Context-Conditioned Structured Simulators with Self-Falsifying Decision Support](https://mlsanity.com/paper/2605.19826/) (2026)
- [SCP-NL2TL: Selective Conformal Prediction with Semantic Verification for Natural Language to Temporal Logic Specifications](https://mlsanity.com/paper/2608.05439/) (2026)
- [Safe to Stop? Risk-Constrained Stopping for Sequential Clinical Diagnosis Agents](https://mlsanity.com/paper/2609.09678/) (2026)
- [Certify or Refuse: A Cross-Model Map for Selective Risk Control with Coverage Floors under Covariate Shift](https://mlsanity.com/paper/2608.10893/) (2026)
- [SafeRestore: Detector-Relative Risk Certificates for Selective Industrial Image Restoration](https://mlsanity.com/paper/2609.03475/) (2026)
- [Signed Lexical Confidence for Risk-Calibrated Intent Routing](https://mlsanity.com/paper/2610.00262/) (2026)

## Abstract (arXiv)

Reliable uncertainty quantification is essential for deploying machine learning systems in high-stakes domains. Conformal prediction provides distribution-free coverage guarantees but often produces overly large prediction sets, limiting its practical utility. To address this issue, we propose textitSelective Conformal Risk Control (SCRC), a unified framework that integrates conformal prediction with selective classification. The framework formulates uncertainty control as a two-stage problem: the first stage selects confident samples for prediction, and the second stage applies conformal risk control on the selected subset to construct calibrated prediction sets. We develop two algorithms under this framework. The first, SCRC-T, preserves exchangeability by computing thresholds jointly over calibration and test samples, offering exact finite-sample guarantees. The second, SCRC-I, is a calibration-only variant that provides PAC-style probabilistic guarantees while being more computational efficient. Experiments on two public datasets show that both methods achieve the target coverage and risk levels, with nearly identical performance, while SCRC-I exhibits slightly more conservative risk control but superior computational practicality. Our results demonstrate that selective conformal risk control offers an effective and efficient path toward compact, reliable uncertainty quantification.