# Fractionally Supervised Classification with Maxima Nominated Samples

arXiv: https://arxiv.org/abs/2604.25145 · HTML: https://mlsanity.com/paper/2604.25145/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 21 references that are in the map.
- First posted on arXiv 28 Apr 2026.

## Builds on (most cited first, 2 of 2)

- [Fractionally-Supervised Classification](https://mlsanity.com/paper/1307.3598/) (2013)
- [On Fractionally-Supervised Classification: Weight Selection and Extension to the Multivariate t-Distribution](https://mlsanity.com/paper/1709.08258/) (2017)

## Abstract (arXiv)

Fractionally supervised classification (FSC) offers a flexible framework for combining labeled and unlabeled data in model-based classification, but existing formulations assume simple random sampling. In many applications, however, the retained observation is an extreme order statistic from a set rather than a randomly selected unit. This is particularly appealing when the target population is rare, since maxima nomination sampling (NS) can enrich the sample with the most informative observations, as in screening, environmental monitoring, repeated testing, and reliability studies. Under such designs, the likelihood function changes fundamentally, and the usual FSC EM construction is no longer valid. We develop FSC for nominated samples by introducing a latent representation that accounts for both the class membership of the observed maximum and the latent composition of the remaining units in the set. The resulting method yields a proper EM algorithm and a coherent weighted-likelihood FSC procedure for NS data. We present the methodology in general form, illustrate it for a rare-event contamination normal mixtures, and show through simulation that it substantially improves on the misspecified alternative by ignoring the extra rank information of such data. A real-data analysis demonstrates its practical value.