TY - GEN
T1 - Fast rates for a kNN classifier robust to unknown asymmetric label noise
AU - Reeve, Henry W. J.
AU - Kaban, Ata
PY - 2019/6/15
Y1 - 2019/6/15
N2 - 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.
AB - 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.
M3 - Conference contribution
VL - 97
T3 - The Proceedings of Machine Learning Research
SP - 5401
EP - 5409
BT - Proceedings of the Thirty-sixth International Conference on Machine Learning (ICML 2019)
T2 - Thirty-sixth International Conference on Machine Learning (ICML 2019)
Y2 - 9 June 2019 through 15 June 2019
ER -