An Unbiased Risk Estimator for Partial Label Learning with Augmented Classes

TL;DR

This article proposes an unbiased risk estimator with theoretical guarantees for Partial Label Learning with Augmented Class (PLLAC), which estimates the distribution of augmented classes by differentiating the distribution of known classes from unlabeled data and can be equipped with arbitrary PLL loss functions.

Abstract

Partial Label Learning (PLL) is a typical weakly supervised learning task, which assumes each training instance is annotated with a set of candidate labels containing the ground-truth label. Recent PLL methods adopt identification-based disambiguation to alleviate the influence of false positive labels and achieve promising performance. However, they require all classes in the test set to have appeared in the training set, ignoring the fact that new classes will keep emerging in real applications. To address this issue, in this paper, we focus on the problem of Partial Label Learning with Augmented Class (PLLAC), where one or more augmented classes are not visible in the training stage but appear in the inference stage. Specifically, we propose an unbiased risk estimator with theoretical guarantees for PLLAC, which estimates the distribution of augmented classes by differentiating the distribution of known classes from unlabeled data and can be equipped with arbitrary PLL loss functions. Besides, we provide a theoretical analysis of the estimation error bound of the estimator, which guarantees the convergence of the empirical risk minimizer to the true risk minimizer as the number of training data tends to infinity. Furthermore, we add a risk-penalty regularization term in the optimization objective to alleviate the influence of the over-fitting issue caused by negative empirical risk. Extensive experiments on benchmark, UCI and real-world datasets demonstrate the effectiveness of the proposed approach.

Figures (5)

• Figure 1: An comparison example between PLL without Augmented Classes and PLL with Augmented Classes, where all the classes in test set are known when PLL without Augmented Classes while augmented classes emerges in test set when PLL with Augmented Classes.
• Figure 2: Test performance on UCI datasets using $\widehat{f}_{\text{un}}$ in the training stage
• Figure 3: Test performance on four UCI datasets when the number of unlabeled instances increases.
• Figure 4: Classification accuracy with different values of the regularization parameter $\lambda$ and $t$.
• Figure 5: (a)-(b): Influence of the mixture proportion $\theta$, (c)-(d): Sensitivity of PLLAC to class prior shift under different mixture proportion