Conformal Margin Risk Minimization: An Envelope Framework for Robust Learning under Label Noise

2026-04-07

AI Summary

This work proposes CMRM, a plug-and-play robust learning framework that operates without prior knowledge such as noise transition matrices, clean subsets, or pretrained features. It introduces, for the first time, the quantile calibration mechanism from conformal prediction into the label noise setting by modeling the confidence gap between observed and competing labels to dynamically select high-confidence samples and suppress potentially mislabeled ones. CMRM constructs a batch-level conformal quantile-based regularizer that seamlessly enhances the robustness of any classification loss. Extensive experiments demonstrate that CMRM improves average accuracy by up to 3.39% across six benchmarks with synthetic and real-world label noise, reduces conformal prediction set size by up to 20.44%, and incurs no performance degradation in noise-free settings.

Abstract

Most methods for learning with noisy labels require privileged knowledge such as noise transition matrices, clean subsets or pretrained feature extractors, resources typically unavailable when robustness is most needed. We propose Conformal Margin Risk Minimization (CMRM), a plug-and-play envelope framework that improves any classification loss under label noise by adding a single quantile-calibrated regularization term, with no privileged knowledge or training pipeline modification. CMRM measures the confidence margin between the observed label and competing labels, and thresholds it with a conformal quantile estimated per batch to focus training on high-margin samples while suppressing likely mislabeled ones. We derive a learning bound for CMRM under arbitrary label noise requiring only mild regularity of the margin distribution. Across five base methods and six benchmarks with synthetic and real-world noise, CMRM consistently improves accuracy (up to +3.39%), reduces conformal prediction set size (up to -20.44%) and does not hurt under 0% noise, showing that CMRM captures a method-agnostic uncertainty signal that existing mechanisms did not exploit.

Problem

• label noise
• robust learning
• conformal prediction
• margin risk
• classification

Innovation

• Conformal Prediction
• Label Noise
• Margin-based Learning
• Robust Learning
• Quantile Calibration