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2005 Fiscal Year Final Research Report Summary

Computational principal on how parts and wholes cooperate and conflict

Research Project

Project/Area Number 15300001
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Fundamental theory of informatics
Research InstitutionTohoku University

Principal Investigator

MARUOKA Akira  Tohoku University, Graduate School of Information Sciences, Professor, 大学院・情報科学研究科, 教授 (50005427)

Co-Investigator(Kenkyū-buntansha) TAKIMOTO Eiji  Tohoku University, Graduate School of Information Sciences, Associate Professor, 大学院・情報科学研究科, 助教授 (50236395)
AMANO Kazuyuki  Tohoku University, Graduate School of Information Sciences, Research Associate, 大学院・情報科学研究科, 助手 (30282031)
Project Period (FY) 2003 – 2005
Keywordsboosting / decision tree / risk information / on line allocation / random projection / clique function / correlation / majority function
Research Abstract

Computational principals on how parts and wholes cooperate and conflict are investigated from the view point of computation theory. Among the results obtained in this project there are followings which we consider important :
1. Using G-entropy, introduced in our paper, we develop an efficient boosting algorithm which is designed by using the top-down decision tree learning algorithm with its splitting criterion based on the G-entropy.
2. The problem of dynamically apportioning resources among a set of options in a worst-case online framework is investigated by introducing information on how high the risk of each option is. We apply the Aggregating Algorithm to this problem and give a tight performance bound.
3. We propose three methods of random projection which randomly maps data represented as vectors to a low dimensional space so that the margin is approximately preserved. Our algorithm turns out to be more efficient than the well known random projection method based on the Johnson-Lindenstrauss Lemma.
4. We derive a superpolynomial lower bound on the size of Boolean circuits that compute the clique function with *(loglog n) negation gates.
5. We show that a single variable function f(x)=x_j has the minimum correlation with the majority function among all fair functions, where the correlation between Boolean functions f and g is defined to be 1-2Pr[f(x)≠g(x)], and a Boolean function f is defined to be fair if Pr[f(x)=1]=1/2.

  • Research Products

    (11 results)

All 2006 2005 2003

All Journal Article (10 results) Book (1 results)

  • [Journal Article] On Learning Monotone Boolean Functions under the Uniform Distribution2006

    • Author(s)
      Kazuyuki Amano, Akira Maruoka
    • Journal Title

      Theoretical Computer Science (Special Issue on ALT 2002) 350(1)

      Pages: 3-12

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Online Allocation with Risk Information2005

    • Author(s)
      Shigeaki Harada, Eiji Takimoto, Akira Maruoka
    • Journal Title

      Lecture Notes in Artifficial Intelligence 3734

      Pages: 343-355

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Random Projection and Its Application to Learning2005

    • Author(s)
      Tatsuya Watanabe, Eiji Takimoto, Kazuyuki Amano, Akira Maruoka
    • Journal Title

      Proceedings of 2005 Workshop on Randomness and Computation

      Pages: 3-4

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] A Superpolynomial Lower Bound for a Circuit Computing the Clique Function with At Most (1/6) log log n Negation Gates2005

    • Author(s)
      Kazuyuki Amano, Akira Maruoka
    • Journal Title

      SIAM Journal on Computing 35(1)

      Pages: 201-216

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Online Allocation with Risk Information2005

    • Author(s)
      Shigeaki Harada, Eiji Takimoto, Akira Maruoka
    • Journal Title

      Lecture Notes in Artificial Intelligence 3734

      Pages: 343-355

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Random Projection and Its Application to Learning2005

    • Author(s)
      Tatsuya Watanabe, Eiji Takimoto, Kazuyuki Amano, Akira Maruoka
    • Journal Title

      Proceedings of 2005 Workshop on Randomness and Computation 3-4

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Theory of Computation, Automata and Languages2005

    • Author(s)
      Akira Maruoka
    • Journal Title

      Saiensu CO. 278

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Top-down decision tree learning as information based boosting2003

    • Author(s)
      Eiji Takimoto, Akira Maruoka
    • Journal Title

      Theoretical Computer Science 292(2)

      Pages: 447-464

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Path Kernels and Multiplicative Updates2003

    • Author(s)
      Eiji Takimoto, Manrfed Warmuth
    • Journal Title

      Journal of Machine Learning Research 4

      Pages: 773-818

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Manrfed Warmuth, Path Kernels and Multiplicative Updates2003

    • Author(s)
      Eiji Takimoto
    • Journal Title

      Journal of Machine Learning Research 4

      Pages: 773-818

    • Description
      「研究成果報告書概要(欧文)」より
  • [Book] 計算理論とオートマトン言語理論2005

    • Author(s)
      丸岡 章
    • Total Pages
      278
    • Publisher
      サイエンス社
    • Description
      「研究成果報告書概要(和文)」より

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Published: 2007-12-13  

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