Toward drawing an atlas of hypothesis classes: Approximating a hypothesis via another hypothesis model

Osamu Maruyama, Takayoshi Shoudai, Satoru Miyano

研究成果: 書籍/レポート タイプへの寄稿会議への寄与

1 被引用数 (Scopus)

抄録

Computational knowledge discovery can be considered to be a complicated human activity concerned with searching for something new from data with computer systems. The optimization of the entire process of computational knowledge discovery is a big challenge in computer science. If we had an atlas of hypothesis classes which describes prior and basic knowledge on relative relationship between the hypothesis classes, it would be helpful in selecting hypothesis classes to be searched in discovery processes. In this paper, to give a foundation for an atlas of various classes of hypotheses, we have defined a measure of approximation of a hypothesis class C1 to another class C2. The hypotheses we consider here are restricted to m-ary Boolean functions. For 0 ≤ ε ≤ 1, we say that C1 is (1−ε)-approximated to C2 if, for every distribution D over {0, 1}m, and for each hypothesis h1 ∈ C1, there exists a hypothesis h2 ∈ C2 such that, with the probability at most ε, we have h1(x) ≠ h2(x) where x ∈ {0, 1}m is drawn randomly and independently according to D. Thus, we can use the approximation ratio of C1 to C2 as an index of how similar C1 is to C2. We discuss lower bounds of the approximation ratios among representative classes of hypotheses like decision lists, decision trees, linear discriminant functions and so on. This prior knowledge would come in useful when selecting hypothesis classes in the initial stage and the sequential stages involved in the entire discovery process.

本文言語英語
ホスト出版物のタイトルDiscovery Science - 5th International Conference, DS 2002, Proceedings
編集者Steffen Lange, Ken Satoh, Carl H. Smith
出版社Springer Verlag
ページ220-232
ページ数13
ISBN(印刷版)3540001883, 9783540001881
DOI
出版ステータス出版済み - 2002
イベント5th International Conference on Discovery Science, DS 2002 - Lubeck, ドイツ
継続期間: 11月 24 200211月 26 2002

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)
2534
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

その他

その他5th International Conference on Discovery Science, DS 2002
国/地域ドイツ
CityLubeck
Period11/24/0211/26/02

!!!All Science Journal Classification (ASJC) codes

  • 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一般

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