当标签缺失模式含信息时,部分标注可能比全标注更优。
Informative Label Missingness in Multiclass Classification Information Geometry and Excess Risk

- 基于似然的理论分析缺失标签中的信息
- 部分标注在特定条件下可降低分类风险
- 适合关注标签缺失机制的研究者
标签缺失若携带信息,会改变完全与部分标注分类器的效率排序。本文针对参数化多分类问题,建立一般性似然理论。通过有效信息分解,分离出因类别缺失导致的信息损失与缺失机制带来的额外信息。进一步推导出在多分类贝叶斯边界活性成对面上的插值过失误差二次展开,表明分类效率取决于信息增益与损失是否与决策边界扰动方向对齐。由此导出分类加权广义特征值准则:在不全局优于完全标注的情况下,部分标注可能具有更小渐近分类风险。在缺失近随机且缺失比例固定时,缺失标签重分布导致的类别信息损失为一阶效应,而缺失模式的有效信息仅在二阶出现。三类二次判别计算、有限样本实验及半合成多分类应用展示了该行为的依赖于场景的特性。
原文摘要 · Abstract (English)
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.
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