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

Osamu Maruyama, Takayoshi Shoudai, Satoru Miyano

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationDiscovery Science - 5th International Conference, DS 2002, Proceedings
EditorsCarl H. Smith, Steffen Lange, Ken Satoh
PublisherSpringer Verlag
Pages220-232
Number of pages13
ISBN (Print)3540001883, 9783540001881
Publication statusPublished - Jan 1 2002
Event5th International Conference on Discovery Science, DS 2002 - Lubeck, Germany
Duration: Nov 24 2002Nov 26 2002

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2534
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other5th International Conference on Discovery Science, DS 2002
CountryGermany
CityLubeck
Period11/24/0211/26/02

    Fingerprint

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Maruyama, O., Shoudai, T., & Miyano, S. (2002). Toward drawing an atlas of hypothesis classes: Approximating a hypothesis via another hypothesis model. In C. H. Smith, S. Lange, & K. Satoh (Eds.), Discovery Science - 5th International Conference, DS 2002, Proceedings (pp. 220-232). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2534). Springer Verlag.