Title: Learning from Complementary Labels,
Abstract: Collecting labeled data is costly and thus a critical bottleneck in
real-world classification tasks. To mitigate this problem, we propose a novel
setting, namely learning from complementary labels for multi-class
classification. A complementary label specifies a class that a pattern does not
belong to. Collecting complementary labels would be less laborious than
collecting ordinary labels, since users do not have to carefully choose the
correct class from a long list of candidate classes. However, complementary
labels are less informative than ordinary labels and thus a suitable approach
is needed to better learn from them. In this paper, we show that an unbiased
estimator to the classification risk can be obtained only from complementarily
labeled data, if a loss function satisfies a particular symmetric condition. We
derive estimation error bounds for the proposed method and prove that the
optimal parametric convergence rate is achieved. We further show that learning
from complementary labels can be easily combined with learning from ordinary
labels (i.e., ordinary supervised learning), providing a highly practical
implementation of the proposed method. Finally, we experimentally demonstrate
the usefulness of the proposed methods.