2005 Fiscal Year Final Research Report Summary
AlgorithmicAnalysis of Statistical Mechanical Heuristics
| Project/Area Number |
14084207
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| Research Category |
Grant-in-Aid for Scientific Research on Priority Areas
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| Allocation Type | Single-year Grants |
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| Review Section |
Science and Engineering
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
WATANABE Osamu Tokyo Institute of Technology, Graduate School of Information Science and Engineering, Professor, 大学院情報理工学研究科, 教授 (80158617)
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| Project Period (FY) |
2002 – 2005
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| Keywords | Average-Case Analysis of Algorithms / Satisfiability Problem / Local Search Algorithms / Pseudo Expectation / Boosting |
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| Research Abstract |
We investigate various heuristics that have been proposed and studied in statistical physics and related areas. Our results are classified into the following three topics.
1. Average-case analysis of local search algorithms:
There are many local search heuristics for satisfiability problems, which have been shown to solve given problems efficiently by, mainly, computer experiments. We proposed an approach for investigating such heuristics as rigorously as possible. One key method of this approach is "pseudo expectation", a way to analyze the average state of relatively simple (but with a large state space) Markov processes.
2. Design method for efficient learning algorithms:
Boosting method has been studied as one of the important approach for designing learning algorithms. We studied the algorithmic aspects of boosting. We proposed "MadaBoost", a simple boosting algorithm that shows better performance for data with noise and outliers. We also proposed an adaptive sampling method as an implementations technique of boosting. On these methods and their statistical investigations have been summarized as a book (in Japanese), which will appear in 2006.
3. Design and analysis of message passing algorithms
Belief propagations have been studied in AI and statistical physics as a promising approach for solving hard combinatorial problems. Based on belief propagation, we derived similar message passing type algorithms for Graph Bisection problem and Max-2SAT problem, well-know NP-hard optimization problems. We also proved that they solve these problems with high probability under certain average-case models.
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