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 - 1995 Jul 5
    Event8th Annual Conference on Computational Learning Theory, COLT 1995 - Santa Cruz, United States
    Duration: 1995 Jul 51995 Jul 8

    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
    Country/TerritoryUnited States
    CitySanta Cruz
    Period95/7/595/7/8

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Artificial Intelligence
    • Software

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