Learning with Proper Partial Labels

TL;DR

This paper introduces a new framework for partial-label learning based on the concept of properness, which requires weaker assumptions, and provides a unified risk estimator with theoretical guarantees and empirical validation.

Contribution

It proposes the proper partial-label learning framework, deriving a risk-consistent unbiased estimator under weaker assumptions than previous methods.

Findings

The estimator is risk-consistent.

The framework includes many previous settings as special cases.

Experimental results validate the effectiveness of the proposed method.

Abstract

Partial-label learning is a kind of weakly-supervised learning with inexact labels, where for each training example, we are given a set of candidate labels instead of only one true label. Recently, various approaches on partial-label learning have been proposed under different generation models of candidate label sets. However, these methods require relatively strong distributional assumptions on the generation models. When the assumptions do not hold, the performance of the methods is not guaranteed theoretically. In this paper, we propose the notion of properness on partial labels. We show that this proper partial-label learning framework requires a weaker distributional assumption and includes many previous partial-label learning settings as special cases. We then derive a unified unbiased estimator of the classification risk. We prove that our estimator is risk-consistent, and we also establish an estimation error bound. Finally, we validate the effectiveness of our algorithm through experiments.