2019 Fiscal Year Final Research Report
Initial value selection and acceleration of the EM algorithm for finite mixture models
| Project/Area Number |
16K00061
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | Okayama University of Science |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
足立 浩平 大阪大学, 人間科学研究科, 教授 (60299055)
飯塚 誠也 岡山大学, 全学教育・学生支援機構, 教授 (60322236)
森 裕一 岡山理科大学, 経営学部, 教授 (80230085)
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| Project Period (FY) |
2016-04-01 – 2020-03-31
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| Keywords | EMアルゴリズム / 加速 / 初期値選択 / 混合モデル |
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| Outline of Final Research Achievements |
The EM algorithm is a general and popular algorithm for finding maximum likelihood estimates from incomplete data due to stability in convergence, simplicity in implementation and applicability in practice, while the algorithm only guarantees local and linear convergence. They are the drawbacks when the EM algorithm is applied to finite mixture models. We tried to develop an initial value selection method to select a suitable initial value such that the EM algorithm starting from the selected value can find an estimate maximizing globally the likelihood function. In order to reduce the total computation time and the number of iterations, we developed an algorithm that accelerates the convergence of the EM algorithm. Moreover, we showed an algorithm to improve the speed of computation of the bootstrap method using the EM algorithm.
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| Free Research Field |
計算機統計学
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| Academic Significance and Societal Importance of the Research Achievements |
画像解析と機械学習などにおいて用いられる大規模データに対して統計モデルを考えるとき，混合モデルを仮定することになる．このモデルのもとでのデータ解析のための数値計算では，短い計算時間で最適な推定値を得ることが求められる．本研究では，統計計算法に用いられるEMアルゴリズムに焦点を当て，計算時間の短縮を図る加速法の開発と，最良な初期値を見つける初期値選択法の開発により，この問題の解決を図る．この研究の応用場面としては，医療診断における画像解析や機械学習等の分野のデータ解析であり，実用価値が高い研究である．
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