# Learning from Uncertainty-dependent Missing Labels for Semi-supervised Classification

arXiv: https://arxiv.org/abs/2608.23960 · HTML: https://mlsanity.com/paper/2608.23960/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 29 references that are in the map.
- First posted on arXiv 25 Aug 2026.

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

- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [MixMatch: A Holistic Approach to Semi-Supervised Learning](https://mlsanity.com/paper/1905.02249/) (2019)
- [Unsupervised Data Augmentation for Consistency Training](https://mlsanity.com/paper/1904.12848/) (2019)
- [A Survey on Deep Semi-supervised Learning](https://mlsanity.com/paper/2103.00550/) (2021)
- [Causality for Machine Learning](https://mlsanity.com/paper/1911.10500/) (2019)
- [An Apparent Paradox: A Classifier Trained from a Partially Classified Sample May Have Smaller Expected Error Rate Than That If the Sample Were Completely Classified](https://mlsanity.com/paper/1910.09189/) (2019)
- [Semi-Supervised Learning of Classifiers from a Statistical Perspective: A Brief Review](https://mlsanity.com/paper/2104.04046/) (2021)

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

- [Large Classification-Risk-Optional Label Acquisition](https://mlsanity.com/paper/2609.06873/) (2026)

## Abstract (arXiv)

Missing labels are usually regarded as a source of information loss in classification. We study a semi-supervised setting in which the probability of label missingness depends on the observed features through posterior classification uncertainty. In this setting, the missingness indicator is not only a record of an unobserved label, but also an observable signal generated by a mechanism linked to the classifier. We develop a likelihood-based information theory for such uncertainty-dependent missing labels. Under correct specification, we derive a Fisher-information decomposition that separates a partial-labeling component from a nonnegative mechanism-curvature term. Under joint misspecification of the label model and the missingness mechanism, we obtain the corresponding Godambe--Eicker--Huber--White sensitivity and sandwich-covariance partitions. We also clarify the relevant complete-data benchmark: favorable missingness can increase information relative to ordinary fully labeled or budget-matched non-informative labeling baselines, but cannot exceed the information in the augmented experiment in which labels and mechanism indicators are both observed. For plug-in classifiers, we connect the information decomposition to margin-based excess-risk bounds. In regular two-component mixture settings this yields the parametric (n-1) excess-risk rate, with constants determined by the nuisance-adjusted information in discriminant directions. Gaussian-mixture calculations and a medical diagnosis example illustrate how uncertainty-dependent labeling mechanisms can improve estimation and classification under a fixed labeling budget.