Learning with Multiple Complementary Labels

TL;DR

This paper introduces a new setting for learning with multiple complementary labels per example, proposing two methods—one decomposing MCLs into single CLs and another deriving an unbiased risk estimator—demonstrating the latter's superior performance.

Contribution

It extends the complementary label learning framework to multiple labels per example and proposes two novel methods, including an unbiased risk estimator with theoretical guarantees.

Findings

The second method outperforms the first in experiments.

Decomposition approach is effective but less accurate.

Unbiased risk estimator provides better learning performance.

Abstract

A complementary label (CL) simply indicates an incorrect class of an example, but learning with CLs results in multi-class classifiers that can predict the correct class. Unfortunately, the problem setting only allows a single CL for each example, which notably limits its potential since our labelers may easily identify multiple CLs (MCLs) to one example. In this paper, we propose a novel problem setting to allow MCLs for each example and two ways for learning with MCLs. In the first way, we design two wrappers that decompose MCLs into many single CLs, so that we could use any method for learning with CLs. However, the supervision information that MCLs hold is conceptually diluted after decomposition. Thus, in the second way, we derive an unbiased risk estimator; minimizing it processes each set of MCLs as a whole and possesses an estimation error bound. We further improve the second way into minimizing properly chosen upper bounds. Experiments show that the former way works well for learning with MCLs but the latter is even better.