Complexity of computing generalized VC-dimensions

研究成果: Conference contribution

1 被引用数 (Scopus)

抄録

In the PAC-learning model, the Vapnik-Chervonenkis (VC) dimension plays the key role to estimate the polynomial-sample learnability of a class of binary functions. For a class of {0,…, m}-valued functions, the notion has been generalized in various ways. This paper investigates the complexity of computing some of generalized VC-dimensions: VC*-dimension, Ψ*-dimension, and ΨG-dimension. For each dimension, we consider a decision problem that is, for a given matrix representing a class F of functions and an integer K, to determine whether the dimension of F is greater than K or not. We prove that the VC*-dimension problem is polynomial-time reducible to the satisfiability problem of length J with O(log2J) variables, which includes the original VC-dimension problem as a special case. We also show that the ΨG-dimension problem is still reducible to the satisfiability problem of length J with O(log2 J), while the Ψ*-dimension problem becomes NP-complete.

本文言語English
ホスト出版物のタイトルMachine Learning
ホスト出版物のサブタイトルECML 1994 - European Conference on Machine Learning, Proceedings
編集者Francesco Bergadano, Luc De Raedt
出版社Springer Verlag
ページ415-418
ページ数4
ISBN(印刷版)9783540578680
DOI
出版ステータスPublished - 1994
外部発表はい
イベントEuropean Conference on Machine Learning, ECML 1994 - Catania, Italy
継続期間: 1994 4 61994 4 8

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
784 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

Other

OtherEuropean Conference on Machine Learning, ECML 1994
国/地域Italy
CityCatania
Period94/4/694/4/8

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

フィンガープリント

「Complexity of computing generalized VC-dimensions」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル