Uniform characterizations of polynomial-query learnabilities

Yosuke Hayashi, Satoshi Matsumoto, Ayumi Shinohara, Masayuki Takeda

Research output: Contribution to journalArticle

Abstract

We consider the exact learning in the query model. We deal with all types of queries introduced by Angluin: membership, equivalence, superset, subset, disjointness and exhaustiveness queries, and their weak (or restricted) versions where no counterexample is returned. For each of all possible combinations of these queries, we uniformly give complete characterizations of boolean concept classes that are learnable using a polynomial number of polynomial-sized queries. Our characterizations show the equivalence between the learnability of a concept class script C sign using queries and the existence of a good query for any subset H of script C sign which is guaranteed to reject a certain fraction of candidate concepts in H regardless of the answer. As a special case for equivalence queries alone, our characterizations directly correspond to the lack of the approximate fingerprint property, which is known to be a sufficient and necessary condition for the learnability using equivalence queries.

Original languageEnglish
Pages (from-to)377-385
Number of pages9
JournalTheoretical Computer Science
Volume292
Issue number2
DOIs
Publication statusPublished - Jan 27 2003

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Learnability
Polynomials
Query
Polynomial
Equivalence
Subset
Fingerprint
Counterexample
Necessary Conditions

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Uniform characterizations of polynomial-query learnabilities. / Hayashi, Yosuke; Matsumoto, Satoshi; Shinohara, Ayumi; Takeda, Masayuki.

In: Theoretical Computer Science, Vol. 292, No. 2, 27.01.2003, p. 377-385.

Research output: Contribution to journalArticle

Hayashi, Yosuke ; Matsumoto, Satoshi ; Shinohara, Ayumi ; Takeda, Masayuki. / Uniform characterizations of polynomial-query learnabilities. In: Theoretical Computer Science. 2003 ; Vol. 292, No. 2. pp. 377-385.
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