## Abstract

We consider the problem of learning k-parities in the online mistake-bound model: given a hidden vector (Formula Presented) where the hamming weight of x is k and a sequence of “questions” (Formula Presented), where the algorithm must reply to each question with (Formula Presented), what is the best trade-off between the number of mistakes made by the algorithm and its time complexity? We improve the previous best result of Buhrman et al. [BGM10] by an (Formula Presented) factor in the time complexity. Next, we consider the problem of learning k-parities in the PAC model in the presence of random classification noise of rate (Formula Presented). Here, we observe that even in the presence of classification noise of non-trivial rate, it is possible to learn k-parities in time better than (Formula Presented), whereas the current best algorithm for learning noisy k-parities, due to Grigorescu et al. [GRV11], inherently requires time (Formula Presented) even when the noise rate is polynomially small.

Original language | English |
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Title of host publication | Computing and Combinatorics - 24th International Conference, COCOON 2018, Proceedings |

Publisher | SPRINGER |

Pages | 542-553 |

Number of pages | 12 |

ISBN (Print) | 9783319947754 |

DOIs | |

Publication status | Published - 1 Jan 2018 |

MoE publication type | A4 Article in a conference publication |

Event | International Computing and Combinatorics Conference - Qing Dao, China Duration: 2 Jul 2018 → 4 Jul 2018 Conference number: 24 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 10976 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | International Computing and Combinatorics Conference |
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Abbreviated title | COCOON |

Country/Territory | China |

City | Qing Dao |

Period | 02/07/2018 → 04/07/2018 |