## Abstract

We investigate the problem of classification in the presence of unknown class-conditional label noise in which the labels observed by the learner have been corrupted with some unknown class dependent probability. In order to obtain finite sample rates, previous approaches to classification with unknown class-conditional label noise have required that the regression function is close to its extrema on sets of large measure. We shall consider this problem in the setting of non-compact metric spaces, where the regression function need not attain its extrema. In this setting we determine the minimax optimal learning rates (up to logarithmic factors). The rate displays interesting threshold behaviour: When the regression function approaches its extrema at a sufficient rate, the optimal learning rates are of the same order as those obtained in the label-noise free setting. If the regression function approaches its extrema more gradually then classification performance necessarily degrades. In addition, we present an adaptive algorithm which attains these rates without prior knowledge of either the distributional parameters or the local

density. This identifies for the first time a scenario in which finite sample rates are achievable in the label noise setting, but they differ from the optimal rates without label noise..

density. This identifies for the first time a scenario in which finite sample rates are achievable in the label noise setting, but they differ from the optimal rates without label noise..

Original language | English |
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Title of host publication | 32nd Annual Conference on Learning Theory (COLT 19) |

Publisher | Proceedings of Machine Learning Research |

Pages | 2624-2651 |

Number of pages | 28 |

Volume | 99 |

Publication status | Published - 17 Aug 2019 |

Event | 32nd Annual Conference on Learning Theory (COLT 19) - Phoenix, Arizona, United States Duration: 25 Jun 2019 → 28 Jun 2019 |

### Publication series

Name | Proceedings of Machine Learning Research |
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Volume | 99 |

ISSN (Electronic) | 2640-3498 |

### Conference

Conference | 32nd Annual Conference on Learning Theory (COLT 19) |
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Country/Territory | United States |

City | Phoenix, Arizona |

Period | 25/06/19 → 28/06/19 |

## Keywords

- Label noise
- minimax rates
- non-parametric classification
- metric spaces