Proper learning algorithm for functions of κ terms under smooth distributions

Yoshifumi Sakai, Eiji Takimoto, Akira Maruoka

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationProceedings of the 8th Annual Conference on Computational Learning Theory, COLT 1995
PublisherAssociation for Computing Machinery, Inc
Pages206-213
Number of pages8
ISBN (Electronic)0897917235, 9780897917230
DOIs
Publication statusPublished - Jul 5 1995
Externally publishedYes
Event8th Annual Conference on Computational Learning Theory, COLT 1995 - Santa Cruz, United States
Duration: Jul 5 1995Jul 8 1995

Publication series

NameProceedings of the 8th Annual Conference on Computational Learning Theory, COLT 1995
Volume1995-January

Other

Other8th Annual Conference on Computational Learning Theory, COLT 1995
CountryUnited States
CitySanta Cruz
Period7/5/957/8/95

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Artificial Intelligence
  • Software

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  • Cite this

    Sakai, Y., Takimoto, E., & Maruoka, A. (1995). Proper learning algorithm for functions of κ terms under smooth distributions. In Proceedings of the 8th Annual Conference on Computational Learning Theory, COLT 1995 (pp. 206-213). (Proceedings of the 8th Annual Conference on Computational Learning Theory, COLT 1995; Vol. 1995-January). Association for Computing Machinery, Inc. https://doi.org/10.1145/225298.225323