## 抄録

We study Barron and Cover's theory (BC theory) in supervised learning. The original BC theory can be applied to supervised learning only approximately and limitedly. Though Barron & Luo (2008) and Chatteijee & Barron (2014a) succeeded in removing the approximation, their idea cannot be essentially applied to supervised learning in general. By solving this issue, we propose an extension of BC theory to supervised learning. The extended theory has several advantages inherited from the original BC theory. First, it holds for finite sample number n. Second, it requires remarkably few assumptions. Third, it gives a justification of the MDL principle in supervised learning. We also derive new risk and regret bounds of lasso with random design as its application. The derived risk bound hold for any finite n without bound-edness of features in contrast to past work. Behavior of the regret bound is investigated by numerical simulations. We believe that this is the first extension of BC theory to general supervised learning without approximation.

本文言語 | 英語 |
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ホスト出版物のタイトル | 33rd International Conference on Machine Learning, ICML 2016 |

出版社 | International Machine Learning Society (IMLS) |

ページ | 2896-2905 |

ページ数 | 10 |

巻 | 4 |

ISBN（電子版） | 9781510829008 |

出版ステータス | 出版済み - 2016 |

イベント | 33rd International Conference on Machine Learning, ICML 2016 - New York City, 米国 継続期間: 6 19 2016 → 6 24 2016 |

### その他

その他 | 33rd International Conference on Machine Learning, ICML 2016 |
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Country | 米国 |

City | New York City |

Period | 6/19/16 → 6/24/16 |

## All Science Journal Classification (ASJC) codes

- Artificial Intelligence
- Software
- Computer Networks and Communications