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

• URL: http://arxiv.org/abs/2608.23960v1
• Date: Tue, 25 Aug 2026 01:40:47 GMT
• Title: Learning from Uncertainty-dependent Missing Labels for Semi-supervised Classification
• Abstract summary: We study a semi-supervised setting in which the probability of label missingness depends on the observed features.<n>We develop a likelihood-based information theory for such uncertainty-dependent missing labels.
• Score: 2.5794915063815664
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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