Proper learning algorithm for functions of κ terms under smooth distributions

Yoshifumi Sakai, Eiji Takimoto, Akira Maruoka

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

7 被引用数 (Scopus)

抄録

Algorithms for learning feasibly Boolean functions from examples are explored. A class of functions we deal with is written as F1 oF2k = {g(f1(v),...fk(v)) g ∈ F1, f1...,fk ∈ F2} for classes F1 and F2 given by somewhat "simple" description. Letting Γ = {0,1}, we denote by F1 and F2 a class of functions from Γk to Γ and that of functions from Γn to Γ, respectively. For exa.mple, let FOr consist of an OR function of k variables, and let Fn be the class of all monomials of n variables. In the distribution free setting, it is known that FORo Fnk, denoted usually k-term DNF, is not learnable unless P≠NP In this paper, we first introduce a probabilistic distribution, called a smooth distribution, which is a generalization of both q-bounded distribution and product distribution, and define the learnability under this distribution. Then, we give an algorithm that properly learns FkoTnk under smooth distribution in polynomial time for constant k, where Fk is the class of all Boolean functions of k variables. The class FkoTnk is called the functions of k terms and although it was shown by Blum and Singh to be learned using DNF as a hypothesis class, it remains open whether it is properly learnable under distribution free setting.

本文言語英語
ホスト出版物のタイトルProceedings of the 8th Annual Conference on Computational Learning Theory, COLT 1995
出版社Association for Computing Machinery, Inc
ページ206-213
ページ数8
ISBN(電子版)0897917235, 9780897917230
DOI
出版ステータス出版済み - 7 5 1995
外部発表はい
イベント8th Annual Conference on Computational Learning Theory, COLT 1995 - Santa Cruz, 米国
継続期間: 7 5 19957 8 1995

出版物シリーズ

名前Proceedings of the 8th Annual Conference on Computational Learning Theory, COLT 1995
1995-January

その他

その他8th Annual Conference on Computational Learning Theory, COLT 1995
国/地域米国
CitySanta Cruz
Period7/5/957/8/95

All Science Journal Classification (ASJC) codes

  • 理論的コンピュータサイエンス
  • 人工知能
  • ソフトウェア

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