Unified framework for learning with label distribution

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 L² 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 L² 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