Gray Learning from Non-IID Data with Out-of-distribution Samples

The quality of the training data annotated by experts cannot be guaranteed, even more so for non-IID data consisting of both in- and out-of-distribution samples (i.e., in-distribution and out-of-distribution samples hold different distributions). Experts may mistakenly annotate out-of-distribution samples the same as in-distribution samples, incurring untrustworthy ground-truth labels. Learning such non-IID data mixing in- and out-of-distribution samples with untrustworthy labels significantly challenges both shallow and deep learning, with no relevant work reported. It would be possible to identify trustworthy complementary labels of a sample indicating which classes it does not belong to, because both in- and out-of-distribution samples do not belong to the classes except those corresponding to the ground-truth label. With this insight, we propose a novel \textit{gray learning} approach to robustly learn from non-IID data with both in- and out-of-distribution samples. Due to the uncertain distributions of training samples, we reject the complementary labels for low-confidence inputs while mapping high-confidence inputs to the ground-truth labels in training. Building on the statistical learning theory, we derive the generalization error which shows that gray learning achieves a tight bound on the non-IID data. Extensive experiments show that our method provides significant improvement over alternative methods from robust statistics.