Semi-Supervised Mixture Models under the Concept of Missing at Radom with Margin Confidence and Aranda Ordaz Function
This work addresses bias and robustness issues in semi-supervised learning for classification tasks, particularly in domains with missing data, but it is incremental as it builds on existing mixture model and missingness mechanism frameworks.
The paper tackles bias in semi-supervised learning with missing labels under a Missing at Random mechanism by modeling missingness probability as a function of classification uncertainty using margin confidence and an Aranda Ordaz link function, resulting in reliable classification performance in realistic scenarios with substantial missing labels.
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.