Fractionally Supervised Classification with Maxima Nominated Samples

TL;DR

This paper extends fractionally supervised classification (FSC) to handle maxima nomination sampling, improving classification in rare-event scenarios by incorporating order statistic information into the EM algorithm.

Contribution

It introduces a novel FSC method tailored for maxima nomination sampling, accounting for the unique likelihood structure and latent class membership.

Findings

The new FSC method outperforms misspecified alternatives in simulations.

Application to real data shows practical effectiveness in rare-event classification.

Method improves classification accuracy by leveraging rank information in NS data.

Abstract

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 Under such designs, the likelihood function changes fundamentally, and the usual FSC EM construction is no longer valid.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.