AlgorithmicAnalysis of Statistical Mechanical Heuristics
Grant-in-Aid for Scientific Research on Priority Areas
|Allocation Type||Single-year Grants|
|Research Institution||Tokyo Institute of Technology|
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)
岩間 一雄 京都大学, 大学院・情報学研究科, 教授 (50131272)
|Project Period (FY)
2002 – 2005
Completed(Fiscal Year 2005)
|Budget Amount *help
¥25,100,000 (Direct Cost : ¥25,100,000)
Fiscal Year 2005 : ¥7,200,000 (Direct Cost : ¥7,200,000)
Fiscal Year 2004 : ¥6,900,000 (Direct Cost : ¥6,900,000)
Fiscal Year 2003 : ¥6,000,000 (Direct Cost : ¥6,000,000)
Fiscal Year 2002 : ¥5,000,000 (Direct Cost : ¥5,000,000)
|Keywords||Average-Case Analysis of Algorithms / Satisfiability Problem / Local Search Algorithms / Pseudo Expectation / Boosting / 確率アルゴリズム / 乱択計算 / 局所探索法 / マルコフ過程 / 近似解析 / サンプリング技法 / 片誤り性 / 確立アルゴリズム / ランダマイズド計算 / 制約解探索問題 / アルゴリズムの状態確率の変化|
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.
Research Products (34results)