# When Does Trimming Help Conformal Prediction? A Retained-Law Diagnostic under Calibration Contamination

arXiv: https://arxiv.org/abs/2605.06204 · HTML: https://mlsanity.com/paper/2605.06204/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 45 references that are in the map.
- First posted on arXiv 7 May 2026.

## Builds on (most cited first, 7 of 7)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [A Conformal Prediction Score that is Robust to Label Noise](https://mlsanity.com/paper/2405.02648/) (2024)
- [Conformal Prediction under Levy-Prokhorov Distribution Shifts: Robustness to Local and Global Perturbations](https://mlsanity.com/paper/2502.14105/) (2025)
- [Exploring the Noise Robustness of Online Conformal Prediction](https://mlsanity.com/paper/2501.18363/) (2025)
- [Conformal Prediction with Cellwise Outliers: A Detect-then-Impute Approach](https://mlsanity.com/paper/2505.04986/) (2025)
- [Probabilistic Inference and Learning with Stein's Method](https://mlsanity.com/paper/2603.07467/) (2026)
- [Noise-Adaptive Conformal Classification with Marginal Coverage](https://mlsanity.com/paper/2501.18060/) (2025)

## Built on by (most cited first, 1 of 1)

- [Self-Poisoning in Adaptive Out-of-Distribution Detection: A Sharp-Threshold Theory and Certified Label-Free Calibration](https://mlsanity.com/paper/2607.21673/) (2026)

## Abstract (arXiv)

Trimming suspicious calibration points is a common response to contamination in conformal prediction. Its effect on clean-target coverage, however, is governed by the retained law induced by trimming, not by the contamination level alone. We analyse fixed-threshold trimming as conditioning rather than purification. It replaces the contaminated calibration law with a retained law, reducing clean-target coverage to a one-dimensional score-CDF transfer problem with an exact finite-sample identity. A componentwise bound on the transfer gap gives a population-level diagnostic. This separates a clean-side covariance cost from a retained-contamination cost, governed by the dirty-to-clean retention ratio. Trimming helps when the anomaly score separates retention probabilities while remaining score-neutral on the clean population. Otherwise, it cannot substantially reduce contamination through the retained mixture coefficient. We also give finite-sample certificate templates that provide numerical guarantees under independent audit.