As a recently arisen framework, Label Distribution Learning (LDL) is one of the most appropriate machine learning paradigms to solve the label ambiguity problems. Due to the high cost, it is intractable to directly collect annotated distribution-level data. Therefore, Label Enhancement (LE) is proposed to obtain the label distribution for training LDL model by mining the information hidden in the logical labels. Accordingly, LE is usually taken as the pre-processing of LDL algorithm to learn with logical labels in previous methods. These two-stage learning methods may reduce the performance of LDL. To this end, we propose a unified framework called $L^2$ which simultaneously conducts Label Enhancement and Label Distribution Learning on samples and logical labels to fully exploit the implicit information for learning optimal LDL model. Specifically, the recovery of label distribution benefits from not only the optimization of the conventional LE objective function but also the feedback of LDL loss. What is more, the recovered distribution labels can be directly applied to the supervision of LDL training in an end-to-end way. Extensive experiments illustrate that $L^2$ can correctly recover the distribution-level data from the logical labels, and the trained LDL model can perform favorably against state-of-the-art LDL algorithms with the recovered distribution data.¹

作为最近出现的框架，标签分发学习（LDL）是解决标签歧义性问题的最合适的机器学习范例之一。由于成本高昂，直接收集带注释的分布级别数据是很棘手的。因此，提出了标签增强（Label Enhancement，LE）技术，通过挖掘隐藏在逻辑标签中的信息来获得用于训练LDL模型的标签分布。因此，通常将LE用作LDL算法的预处理，以便在以前的方法中使用逻辑标记进行学习。这两个阶段的学习方法可能会降低LDL的性能。为此，我们提出了一个统一的框架，称为${\mathrm{大号}}^{\mathrm{2个}}$其同时进行大号阿贝尔增强和大号阿贝尔分布学习样本和逻辑标签充分利用用于学习最佳LDL模型隐含信息。具体而言，标签分布的恢复不仅受益于常规LE目标函数的优化，而且受益于LDL丢失的反馈。而且，恢复的分发标签可以以端到端的方式直接应用于LDL培训的监督。大量实验表明${\mathrm{大号}}^{\mathrm{2个}}$可以正确地从逻辑标签中恢复分发级别的数据，并且经过训练的LDL模型可以很好地胜过具有恢复的分发数据的最新LDL算法。^1个