| Project/Area Number |
16K00044
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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 | Tokyo Institute of Technology (2017-2019)
Nagoya University (2016) |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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| Keywords | 機械学習 / 数理統計学 / 最適化 / 変数選択 / ロバスト統計 / ロバスト |
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| Outline of Final Research Achievements |
The purpose is to promote research from a unified viewpoint of optimization of non-convex loss functions for problems of statistical learning such as robust estimation and sparse modeling. We constructed a practically efficient learning algorithm and built the mathematical foundation of non-convex learning. In particular, for robust support vector machines with a non-convex loss function, we mathematically analyzed the properties of the local optimal solutions. Useful mathematical concepts such as breakdown point have been applied to analyze the properties of learning algorithms with non-convex functions for classification tasks. As a result, it was clarified that even a local optimal solution theoretically achieves high prediction accuracy even under strong contamination Furthermore, we proposed a statistical analysis method for discrete data, and showed that the non-convex optimization can be efficiently calculated by replacing it with local calculation.
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| Academic Significance and Societal Importance of the Research Achievements |
非凸損失を用いる統計的学習は一般に，統計的性質は優れているが，最適化のための計算が非常に困難であることが知られている．最適化の困難を解決することができれば，，データに大きなノイズが含まれる場合でも，非常にロバストな統計的推論を高い計算効率で実行することが可能になる．本研究では，判別分析や離散確率分布の推定という重要な問題クラスに対して，非凸損失による効率的な学習アルゴリズムを提案し，その数理的性質を詳しく研究した．その結果，理論，実装の両面から提案法の有効性を確認することができた．
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