# Analysis of Estimating the Bayes Rule for Gaussian Mixture Models with a Specified Missing-Data Mechanism

arXiv: https://arxiv.org/abs/2210.13785 · HTML: https://mlsanity.com/paper/2210.13785/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 40 references that are in the map.
- First posted on arXiv 25 Oct 2022.

## Builds on (most cited first, 3 of 3)

- [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)
- [Optimal responsiveness and collective oscillations emerging from the heterogeneity of inhibitory neurons](https://mlsanity.com/paper/2005.05596/) (2020)

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

- [Semi-Supervised Mixture Models under the Concept of Missing at Radom with Margin Confidence and Aranda Ordaz Function](https://mlsanity.com/paper/2601.14631/) (2026)

## Abstract (arXiv)

Semi-supervised learning (SSL) approaches have been successfully applied in a wide range of engineering and scientific fields. This paper investigates the generative model framework with a missingness mechanism for unclassified observations, as introduced by Ahfock and McLachlan(2020). We show that in a partially classified sample, a classifier using Bayes rule of allocation with a missing-data mechanism can surpass a fully supervised classifier in a two-class normal homoscedastic model, especially with moderate to low overlap and proportion of missing class labels, or with large overlap but few missing labels. It also outperforms a classifier with no missing-data mechanism regardless of the overlap region or the proportion of missing class labels. Our exploration of two- and three-component normal mixture models with unequal covariances through simulations further corroborates our findings. Finally, we illustrate the use of the proposed classifier with a missing-data mechanism on interneuronal and skin lesion datasets.