2005 Fiscal Year Final Research Report Summary
Computational principal on how parts and wholes cooperate and conflict
| Project/Area Number |
15300001
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Fundamental theory of informatics
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| Research Institution | Tohoku University |
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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)
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| 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)
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| Project Period (FY) |
2003 – 2005
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| Keywords | boosting / decision tree / risk information / on line allocation / random projection / clique function / correlation / majority function |
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| 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.
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