Learning with Proper Partial Labels

Abstract

Partial-label learning is a kind of weakly-supervised learning with inexact labels, where for each training example, we are given a set of candidate labels instead of only one true label. Recently, various approaches on partial-label learning have been proposed under different generation models of candidate label sets. However, these methods require relatively strong distributional assumptions on the generation models. When the assumptions do not hold, the performance of the methods is not guaranteed theoretically. In this paper, we propose the notion of properness on partial labels. We show that this proper partial-label learning framework includes many previous partial-label learning settings as special cases. We then derive a unified unbiased estimator of the classification risk. We prove that our estimator is risk-consistent by obtaining its estimation error bound. Finally, we validate the effectiveness of our algorithm through experiments.

Progressive Purification for Instance-Dependent Partial Label Learning

“…However, all of them made the instance-independent assumption for analyzing the statistic consistency. Wu and Sugiyama [32] proposed a framework that unifies the formalization of multiple generation processes under the instance-independent assumption.…”

“…A large number of deep PLL algorithms have recently emerged that aimed to design regularizers [37,38,23] or network architectures [29] for PLL data. Further, there are some PLL works that provided theoretical guarantees while making their methods compatible with deep networks [22,11,31,32]. We observe that these existing theoretical works have focused on the instance-independent setting where the generation process of partial labels is homogeneous across training examples.…”