Proper Learning Algorithm for Functions of k Terms under Smooth Distributions

Yoshifumi Sakai, Eiji Takimoto, Akira Maruoka

Research output: Contribution to journalArticlepeer-review

2 Citations (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.

Original languageEnglish
Pages (from-to)188-204
Number of pages17
JournalInformation and Computation
Issue number2
Publication statusPublished - 1999 Aug 1


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