Learning with Bounded Instance- and Label-dependent Label Noise

TL;DR

This paper addresses learning in the presence of bounded instance- and label-dependent label noise, introducing a new concept of distilled examples and proposing an algorithm with theoretical guarantees that demonstrates effectiveness on synthetic and real data.

Contribution

It introduces the concept of distilled examples and proposes a robust learning algorithm with theoretical guarantees for bounded ILN, a less-studied noise type.

Findings

The proposed algorithm effectively handles BILN in experiments.

Classifiers trained on distilled examples converge to the Bayes optimal classifier.

Empirical results show robustness of the method on real-world datasets.

Abstract

Instance- and Label-dependent label Noise (ILN) widely exists in real-world datasets but has been rarely studied. In this paper, we focus on Bounded Instance- and Label-dependent label Noise (BILN), a particular case of ILN where the label noise rates -- the probabilities that the true labels of examples flip into the corrupted ones -- have upper bound less than $1$. Specifically, we introduce the concept of distilled examples, i.e. examples whose labels are identical with the labels assigned for them by the Bayes optimal classifier, and prove that under certain conditions classifiers learnt on distilled examples will converge to the Bayes optimal classifier. Inspired by the idea of learning with distilled examples, we then propose a learning algorithm with theoretical guarantees for its robustness to BILN. At last, empirical evaluations on both synthetic and real-world datasets show effectiveness of our algorithm in learning with BILN.