Fast Rates for a kNN Classifier Robust to Unknown Asymmetric Label Noise

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Colleges, School and Institutes

Abstract

We consider classification in the presence of classdependent asymmetric label noise with unknown noise probabilities. In this setting, identifiability conditions are known, but additional assumptions were shown to be required for finite sample rates, and so far only the parametric rate has been obtained. Assuming these identifiability conditions, together with a measure-smoothness condition on the regression function and Tsybakov’s margin condition, we show that the Robust kNN classifier of Gao et al. attains, the mini-max optimal rates of the noise-free setting, up to a log factor, even when trained on data with unknown asymmetric label noise. Hence, our results provide a solid theoretical backing for this empirically successful algorithm. By contrast the standard kNN is not even consistent in the setting of asymmetric label noise. A key idea in our analysis is a simple kNN based method for estimating the maximum of a function that requires far less assumptions than existing mode estimators do, and which may be of independent interest for noise proportion estimation and randomised optimisation problems.

Details

Original languageEnglish
Title of host publicationProceedings of the Thirty-sixth International Conference on Machine Learning (ICML 2019)
Publication statusAccepted/In press - 22 Apr 2019
EventThirty-sixth International Conference on Machine Learning (ICML 2019) - Long Beach, CA, United States
Duration: 9 Jun 201915 Jun 2019

Publication series

NameThe Proceedings of Machine Learning Research
Volume97
ISSN (Electronic)2640-3498

Conference

ConferenceThirty-sixth International Conference on Machine Learning (ICML 2019)
CountryUnited States
CityLong Beach, CA
Period9/06/1915/06/19