Learning from Complementary Labels

TL;DR

This paper introduces a new learning paradigm using complementary labels, which specify classes a data point does not belong to, enabling less labor-intensive data collection for multi-class classification.

Contribution

It proposes an unbiased risk estimator from complementarily labeled data, derives error bounds, and demonstrates practical integration with traditional supervised learning.

Findings

Unbiased risk estimator is achievable with a symmetric loss function.

The method achieves optimal parametric convergence rates.

Experimental results validate the effectiveness of 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.