Proper Learning Algorithm for Functions of k Terms under Smooth Distributions

Yoshifumi Sakai, Eiji Takimoto, Akira Maruoka

研究成果: Contribution to journalArticle査読

2 被引用数 (Scopus)


In this paper, we introduce a probabilistic distribution, called a smooth distribution, which is a generalization of variants of the uniform distribution such as q-bounded distribution and product distribution. Then, we give an algorithm that, under the smooth distribution, properly learns the class of functions of k terms given as ℱk ○ script T signkn = {g(f1(v), ..., fk(v))\g∈ ℱk, f1, ..., fk ∈ script T signn} in polynomial time for constant k, where ℱk is the class of all Boolean functions of k variables and sript T signn is the class of terms over n variables. Although class ℱk ○ script T signkn was shown by Blum and Singh to be learned using DNF as the hypothesis class, it has remained open whether it is properly learnable under a distribution-free setting.

ジャーナルInformation and Computation
出版ステータス出版済み - 8 1 1999

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Computer Science Applications
  • Computational Theory and Mathematics

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