On the Robustness of Average Losses for Partial-Label Learning

Partial-label (PL) learning is a typical weakly supervised classification problem, where a PL of an instance is a set of candidate labels such that a fixed but unknown candidate is the true label. For PL learning, there are two lines of research: (a) the identification-based strategy (IBS) purifies each label set and extracts the true label; (b) the average-based strategy (ABS) treats all candidates equally for training. In the past two decades, IBS was a much hotter topic than ABS, since it was believed that IBS is more promising. In this paper, we theoretically analyze ABS and find it also promising in the sense of the robustness of its loss functions. Specifically, we consider five problem settings for the generation of clean or noisy PLs, and we prove that average PL losses with bounded multi-class losses are always robust under mild assumptions on the domination of true labels, while average PL losses with unbounded multi-class losses (e.g., the cross-entropy loss) may not be robust. We also conduct experiments to validate our theoretical findings. Note that IBS is heuristic, and we cannot prove its robustness by a similar proof technique; hence, ABS is more advantageous from a theoretical point of view, and it is worth paying attention to the design of more advanced PL learning methods following ABS.