# Confidence on the Focal: Conformal Prediction with Selection-Conditional Coverage

arXiv: https://arxiv.org/abs/2403.03868 · HTML: https://mlsanity.com/paper/2403.03868/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 58 references that are in the map.
- First posted on arXiv 6 Mar 2024.

## Builds on (most cited first, 24 of 24)

- [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)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Robots That Ask For Help: Uncertainty Alignment for Large Language Model Planners](https://mlsanity.com/paper/2307.01928/) (2023)
- [Testing for Outliers with Conformal p-values](https://mlsanity.com/paper/2104.08279/) (2021)
- [Exact post-selection inference, with application to the lasso](https://mlsanity.com/paper/1311.6238/) (2013)
- [Selection by Prediction with Conformal p-values](https://mlsanity.com/paper/2210.01408/) (2022)
- [Exact Post-Selection Inference for Sequential Regression Procedures](https://mlsanity.com/paper/1401.3889/) (2014)
- [An Extensive Data Processing Pipeline for MIMIC-IV](https://mlsanity.com/paper/2204.13841/) (2022)
- [Model-free selective inference under covariate shift via weighted conformal p-values](https://mlsanity.com/paper/2307.09291/) (2023)
- [Integrative conformal p-values for powerful out-of-distribution testing with labeled outliers](https://mlsanity.com/paper/2208.11111/) (2022)
- [Derandomized Novelty Detection with FDR Control via Conformal E-values](https://mlsanity.com/paper/2302.07294/) (2023)
- [Post-selection inference for e-value based confidence intervals](https://mlsanity.com/paper/2203.12572/) (2022)
- [Conformal Drug Property Prediction with Density Estimation under Covariate Shift](https://mlsanity.com/paper/2310.12033/) (2023)
- [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)
- [Unifying approach to selective inference with applications to cross-validation](https://mlsanity.com/paper/1703.06559/) (2017)
- [A (tight) upper bound for the length of confidence intervals with conditional coverage](https://mlsanity.com/paper/2007.12448/) (2020)
- [Post-selection Inference for Conformal Prediction: Trading off Coverage for Precision](https://mlsanity.com/paper/2304.06158/) (2023)
- [Conformalized Selective Regression](https://mlsanity.com/paper/2402.16300/) (2024)
- [Post-selection point and interval estimation of signal sizes in Gaussian samples](https://mlsanity.com/paper/1405.3340/) (2014)
- [An Exact Sampler for Inference after Polyhedral Model Selection](https://mlsanity.com/paper/2308.10346/) (2023)
- [Hybrid Confidence Intervals for Informative Uniform Asymptotic Inference After Model Selection](https://mlsanity.com/paper/2011.12873/) (2020)

## Built on by (most cited first, 14 of 14)

- [Conformal Alignment: Knowing When to Trust Foundation Models with Guarantees](https://mlsanity.com/paper/2405.10301/) (2024)
- [Conformal Prediction for Natural Language Processing: A Survey](https://mlsanity.com/paper/2405.01976/) (2024)
- [Selecting informative conformal prediction sets with false coverage rate control](https://mlsanity.com/paper/2403.12295/) (2024)
- [A Joint Finite-Sample Certificate for Adaptive Selective Conformal Risk Control](https://mlsanity.com/paper/2606.08517/) (2026)
- [Powerful batch conformal prediction for classification](https://mlsanity.com/paper/2411.02239/) (2024)
- [Calibrated Predictive Lower Bounds on Time-to-Unsafe-Sampling in LLMs](https://mlsanity.com/paper/2506.13593/) (2025)
- [Online Conformal Selection with Accept-to-Reject Changes](https://mlsanity.com/paper/2508.13838/) (2025)
- [Conformal Risk-Averse Decision Making with Action Conditional Guarantee](https://mlsanity.com/paper/2606.05551/) (2026)
- [Dual-Splitting Conformal Prediction for Multi-Step Time Series Forecasting](https://mlsanity.com/paper/2503.21251/) (2025)
- [Elements of Conformal Prediction](https://mlsanity.com/paper/2603.23923/) (2026)
- [Quantifying and Improving Adaptivity in Conformal Prediction through Input Transformations](https://mlsanity.com/paper/2511.11472/) (2025)
- [Online Selective Conformal Prediction with Asymmetric Rules: A Permutation Test Approach](https://mlsanity.com/paper/2602.10018/) (2026)
- [Goal-Oriented Lower-Tail Calibration of Gaussian Processes for Bayesian Optimization](https://mlsanity.com/paper/2605.20145/) (2026)
- [When May a Model Replace the Experiment? Audits, Licenses, and the Price of Trust in Surrogate-Driven Design](https://mlsanity.com/paper/2608.01378/) (2026)

## Abstract (arXiv)

Conformal prediction builds marginally valid prediction intervals that cover the unknown outcome of a randomly drawn test point with a prescribed probability. However, in practice, data-driven methods are often used to identify specific test unit(s) of interest, requiring uncertainty quantification tailored to these focal units. In such cases, marginally valid conformal prediction intervals may fail to provide valid coverage for the focal unit(s) due to selection bias. This paper presents a general framework for constructing a prediction set with finite-sample exact coverage, conditional on the unit being selected by a given procedure. The general form of our method accommodates arbitrary selection rules that are invariant to the permutation of the calibration units, and generalizes Mondrian Conformal Prediction to multiple test units and non-equivariant classifiers. We also work out computationally efficient implementation of our framework for a number of realistic selection rules, including top-K selection, optimization-based selection, selection based on conformal p-values, and selection based on properties of preliminary conformal prediction sets. The performance of our methods is demonstrated via applications in drug discovery and health risk prediction.