发表机构
Dipartimento di Scienze Statistiche, Università di Padova; School of Mathematics and Physics, The University of Queensland（帕多瓦大学统计科学系; 昆士兰大学数学与物理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对多分类分类的信息性标签缺失现象，建立基于似然的理论，推导插件超额风险的二次展开，提出分类加权广义特征值准则，通过多类判别计算和实验验证其相关行为。
AI 中文摘要
信息性标签缺失会改变完全标记分类器与部分标记分类器之间通常的效率排序，因为标签缺失模式本身可能携带关于分类模型的信息。我们针对参数化多分类分类中的这一现象建立了通用的基于似然的理论。一种有效信息分解方法将不可用类成员身份损失的信息与标签缺失机制贡献的信息分离开来。随后，我们推导了插件超额风险在多分类贝叶斯边界的活跃成对面上的二次展开，表明分类效率取决于信息增益和损失如何与扰动决策边界的方向对齐。这产生了一种分类加权广义特征值准则，根据该准则，信息性部分分类可能具有更小的渐近分类风险，而无需在Fisher信息上全局主导完全分类。在接近完全随机缺失的情况下，当边际标签缺失比例固定时，标签缺失的重新分配会在一阶改变损失的类标签信息，而来自缺失模式的有效信息仅在二阶出现。三类二次判别计算、有限样本实验以及半合成多分类应用说明了由此产生的依赖于 regime 的行为。
英文摘要
Informative label missingness can change the usual efficiency ordering between completely and partially labelled classifiers because the pattern of missing labels may itself carry information about the classification model. We develop a general likelihood-based theory for this phenomenon in parametric multiclass classification. An efficient-information decomposition separates information lost through unavailable class memberships from information contributed by the missing-label mechanism. We then derive a quadratic expansion of plug-in excess risk over the active pairwise faces of the multiclass Bayes boundary, showing that classification efficiency depends on how information gains and losses align with directions that perturb the decision boundary. This yields a classification-weighted generalized-eigenvalue criterion under which informative partial classification may have smaller asymptotic classification risk without globally dominating complete classification in Fisher information. Near missing completely at random, with the marginal missing-label proportion fixed, redistribution of missing labels changes lost class-label information at first order, whereas efficient information from the missingness pattern appears only at second order. Three-class quadratic discriminant calculations, finite-sample experiments, and a semi-synthetic multiclass application illustrate the resulting regime-dependent behaviour.
