Learning with Biased Complementary Labels

In this paper we study the classi cation problem in which we have access to easily obtainable surrogate for the true labels, namely complementary labels, which specify classes that observations do not belong to. For example, if one is familiar with monkeys but not meerkats, a meerkat is easily identi ed as not a monkey, so “monkey” is annotated to the meerkat as a complementary label. Speci cally, let Y and Ȳ be the true and complementary labels, respectively. We rst model the annotation of complementary labels via the transition probabilities P (Ȳ = i|Y = j), i 6= j ∈ {1, · · · , c}, where c is the number of classes. All the previous methods implicitly assume that the transition probabilities P (Ȳ = i|Y = j) are identical, which is far from true in practice because humans are biased toward their own experience. For example, if a person is more familiar with monkey than prairie dog when providing complementary labels for meerkats, he/she is more likely to employ “monkey” as a complementary label. We therefore reason that the transition probabilities will be di erent. In this paper, we address three fundamental problems raised by learning with biased complementary labels. (1) How to estimate the transition probabilities? (2) How to modify the traditional loss functions and extend standard deep neural network classi ers to learn with biased complementary labels? (3) Does the classi er learned from examples with complementary labels by our proposed method converge to the optimal one learned from examples with true labels? Comprehensive experiments on MNIST, CIFAR10, CIFAR100, and Tiny ImageNet empirically validate the superiority of the proposed method to the current state-of-the-art methods with accuracy gains of over 10%. ∗UBTECH Sydney AI Centre and the School of Information Technologies in the Faculty Engineering and Information Technologies at The University of Sydney, NSW, 2006, Australia, [email protected], [email protected], [email protected] †Department of Biomedical Informatics, University of Pittsburgh,[email protected] 1 ar X iv :1 71 1. 09 53 5v 2 [ st at .M L ] 3 D ec 2 01 7 Not “monkey” Not “prairie dog” Not “meerkat” Complementary Label True Label Meerkat Monkey Prairie Dog Figure 1: A comparison between true labels (top) and complementary labels (bottom).