# Informative missingness and its implications in semi-supervised learning

arXiv: https://arxiv.org/abs/2512.04392 · HTML: https://mlsanity.com/paper/2512.04392/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 9 references that are in the map.
- First posted on arXiv 4 Dec 2025.

## Builds on (most cited first, 4 of 4)

- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [A Survey on Deep Semi-supervised Learning](https://mlsanity.com/paper/2103.00550/) (2021)
- [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)

- [Semi-Supervised Classification with Informative Missing Labels in Weibull Mixture Models](https://mlsanity.com/paper/2609.00774/) (2026)

## Abstract (arXiv)

Semi-supervised learning (SSL) constructs classifiers using both labelled and unlabelled data. It leverages information from labelled samples, whose acquisition is often costly or labour-intensive, together with unlabelled data to enhance prediction performance. This defines an incomplete-data problem, which statistically can be formulated within the likelihood framework for finite mixture models that can be fitted using the expectation-maximisation (EM) algorithm. Ideally, one would prefer a completely labelled sample, as one would anticipate that a labelled observation provides more information than an unlabelled one. However, when the mechanism governing label absence depends on the observed features or the class labels or both, the missingness indicators themselves contain useful information. In certain situations, the information gained from modelling the missing-label mechanism can even outweigh the loss due to missing labels, yielding a classifier with a smaller expected error than one based on a completely labelled sample analysed. This improvement arises particularly when class overlap is moderate, labelled data are sparse, and the missingness is informative. Modelling such informative missingness thus offers a coherent statistical framework that unifies likelihood-based inference with the behaviour of empirical SSL methods.