Biased Complementary-Label Learning Without True Labels

In complementary-label learning (CLL), the complementary transition matrix, denoting the probabilities that true labels flip into complementary labels (CLs) which specify classes observations do not belong to, is crucial to building statistically consistent classifiers. Most existing works implicitly assume that the transition probabilities are identical, which is not true in practice and may lead to undesirable bias in solutions. Few recent works have extended the problem to a biased setting but limit their explorations to modeling the transition matrix by exploiting the complementary class posteriors of anchor points (i.e., instances that almost certainly belong to a specific class). However, due to the severe corruption and unevenness of biased CLs, both anchor points and complementary class posteriors are difficult to predict accurately in the absence of true labels. In this article, rather than directly predicting these two error-prone items, we instead propose a divided-T estimator as an alternative to effectively learn transition matrices from only biased CLs. Specifically, we exploit semantic clustering to mitigate the adverse effects arising from CLs. By introducing the learned semantic clusters as an intermediate class, we factorize the original transition matrix into the product of two easy-to-estimate matrices that are not reliant on the two error-prone items. Both theoretical analyses and empirical results justify the effectiveness of the divided-
$T$
estimator for estimating transition matrices under a mild assumption. Experimental results on benchmark datasets further demonstrate that the divided-
$T$
estimator outperforms state-of-the-art (SOTA) methods by a substantial margin.