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

2026-01-21

AI Summary

This study addresses the estimation bias and degraded classification performance of semi-supervised Gaussian mixture models under missing-at-random (MAR) label scenarios. To mitigate these issues, the authors propose a novel approach that jointly models the data generation process and the label missing mechanism. Specifically, the probability of a label being missing is modeled as a function of classification uncertainty, quantified via marginal confidence. An Aranda–Ordaz link function is introduced to flexibly capture the asymmetric relationship between this uncertainty and the missingness probability. Parameter estimation and label imputation are carried out through an Expectation/Conditional Maximization (ECM) algorithm. Experimental results demonstrate that, under high proportions of MAR missing labels, the proposed method significantly improves classification accuracy and robustness, effectively alleviating the systematic bias induced by ignoring the missingness mechanism.

Technology Category

• Machine Learning: Semi-Supervised Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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.

Problem

• Semi-Supervised Learning
• Missing at Random
• Gaussian Mixture Model
• Classification Uncertainty
• Label Missingness

Innovation

• Semi-supervised learning
• Missing at Random
• Gaussian Mixture Model
• Aranda Ordaz link function
• Margin confidence