Semi-Supervised Mixture Models under the Concept of Missing at Radom with Margin Confidence and Aranda Ordaz Function

TL;DR

This paper introduces a semi-supervised Gaussian mixture model framework that explicitly models missing data mechanisms using margin confidence and the Aranda Ordaz function, improving classification robustness under MAR conditions.

Contribution

It proposes a novel approach combining margin confidence and AO function to model missingness, along with an ECM algorithm for joint parameter estimation and label imputation.

Findings

Enhances classification accuracy in MAR scenarios with missing labels.

Reduces bias caused by ignoring missingness mechanisms.

Provides a robust semi-supervised learning framework.

Abstract

This paper presents a semi-supervised learning framework for Gaussian mixture modelling under a Missing at Random (MAR) mechanism. The method explicitly parameterizes the missingness mechanism by modelling the probability of missingness as a function of classification uncertainty. To quantify classification uncertainty, we introduce margin confidence and incorporate the Aranda Ordaz (AO) link function to flexibly capture the asymmetric relationships between uncertainty and missing probability. Based on this formulation, we develop an efficient Expectation Conditional Maximization (ECM) algorithm that jointly estimates all parameters appearing in both the Gaussian mixture model (GMM) and the missingness mechanism, and subsequently imputes the missing labels by a Bayesian classifier derived from the fitted mixture model. This method effectively alleviates the bias induced by ignoring the missingness mechanism while enhancing the robustness of semi-supervised learning. The resulting uncertainty-aware framework delivers reliable classification performance in realistic MAR scenarios with substantial proportions of missing labels.