基于不确定性建模的半监督混合模型，提升缺失标签场景下的分类可靠性
Semi-Supervised Mixture Models under the Concept of Missing at Radom with Margin Confidence and Aranda Ordaz Function
- 用分类不确定性的边际置信度和阿兰达-奥尔达兹函数建模缺失机制
- 在缺失标签占比高的情况下仍保持稳定分类性能，误差显著降低
- 适合标签不完整的真实数据场景，尤其适用于医疗、金融等高风险领域
本文提出一种在缺失随机（MAR）机制下进行高斯混合模型半监督学习的框架。通过将缺失概率建模为分类不确定性的函数，显式参数化缺失机制。为量化不确定性，引入边际置信度，并采用阿兰达-奥尔达兹（Aranda Ordaz, AO）链接函数灵活捕捉不确定性和缺失概率之间的非对称关系。基于此构建高效的期望条件最大化（ECM）算法，联合估计高斯混合模型（GMM）与缺失机制中的所有参数，并利用拟合模型的贝叶斯分类器对缺失标签进行填补。该方法有效缓解了忽略缺失机制带来的偏差，提升了半监督学习的鲁棒性，在缺失标签比例较高的真实MAR场景中表现可靠。
原文摘要 · Abstract (English)
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.
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