解决噪声标签下的排序估计问题，用概率方法建模标签不确定性。
Stochastic Order Learning: An Approach to Rank Estimation Using Noisy Data
- 将噪声排序标签建模为随机序问题，每个样本有多个可能排名。
- 提出双目标学习框架，同时优化实例与中心的区分性和概率排序关系。
- 在多种噪声类型下表现稳定，适合标签不准确的场景。
在标签噪声下进行排序估计是一个基本挑战，因为序数标注常表现出结构化不确定性，而非简单的标签错误。本文将带噪声序数标签的排序估计重新建模为一个随机序问题，其中每个实例本质上关联多个合理排名，而非单一确定性标签。基于此，我们提出了随机序学习（SOL）框架，通过两个互补目标捕捉序数标签的不确定性：判别性损失用于构建实例与中心之间的交互结构，随机序损失则强制实例间的概率排序关系。在多个不同数据集上的大量实验表明，SOL能在各种类型和程度的标签噪声下实现可靠的排序估计。源代码可在 https://github.com/cwlee00/SOL 获取。
原文摘要 · Abstract (English)
Rank estimation under label noise poses a fundamental challenge, as ordinal annotations often exhibit structured uncertainty rather than simple label corruption. In this paper, we reformulate rank estimation with noisy ordinal labels as a stochastic ordering problem, in which each instance is inherently associated with multiple plausible ranks instead of a single deterministic label. Based on this view, we propose stochastic order learning (SOL), a learning framework that captures ordinal label uncertainty and learns an embedding space through two complementary objectives: a discriminative loss that structures instance--centroid interactions and a stochastic order loss that enforces probabilistic ordering relations between instances. Extensive experiments across diverse datasets demonstrate that SOL enables reliable rank estimation under various types and levels of label noise. The source code is available at https://github.com/cwlee00/SOL.
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