Fast Rates for a kNN Classifier Robust to Unknown Asymmetric Label Noise
This addresses robust classification for machine learning practitioners dealing with noisy labels, offering a theoretical foundation for an existing method.
The paper tackles classification with unknown asymmetric label noise by showing that the Robust kNN classifier achieves minimax optimal rates, up to a log factor, under identifiability, measure-smoothness, and margin conditions, providing theoretical backing for an empirically successful algorithm.
We consider classification in the presence of class-dependent 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 minimax 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.