### Abstract

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.

Original language | English |
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Title of host publication | 33rd International Conference on Machine Learning, ICML 2016 |

Publisher | International Machine Learning Society (IMLS) |

Pages | 2896-2905 |

Number of pages | 10 |

Volume | 4 |

ISBN (Electronic) | 9781510829008 |

Publication status | Published - 2016 |

Event | 33rd International Conference on Machine Learning, ICML 2016 - New York City, United States Duration: Jun 19 2016 → Jun 24 2016 |

### Other

Other | 33rd International Conference on Machine Learning, ICML 2016 |
---|---|

Country | United States |

City | New York City |

Period | 6/19/16 → 6/24/16 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Artificial Intelligence
- Software
- Computer Networks and Communications

### Cite this

*33rd International Conference on Machine Learning, ICML 2016*(Vol. 4, pp. 2896-2905). International Machine Learning Society (IMLS).

**Barron and cover's theory in supervised learning and its application to lasso.** / Kawakita, Masanori; Takeuchi, Junnichi.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*33rd International Conference on Machine Learning, ICML 2016.*vol. 4, International Machine Learning Society (IMLS), pp. 2896-2905, 33rd International Conference on Machine Learning, ICML 2016, New York City, United States, 6/19/16.

}

TY - GEN

T1 - Barron and cover's theory in supervised learning and its application to lasso

AU - Kawakita, Masanori

AU - Takeuchi, Junnichi

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

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M3 - Conference contribution

AN - SCOPUS:84998773575

VL - 4

SP - 2896

EP - 2905

BT - 33rd International Conference on Machine Learning, ICML 2016

PB - International Machine Learning Society (IMLS)

ER -