2020 Fiscal Year Final Research Report
Understanding and developing deep learning as estimation procedures of the high-dimensional parameter
| Project/Area Number |
18K11208
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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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| Review Section |
Basic Section 60030:Statistical science-related
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| Research Institution | The Institute of Statistical Mathematics |
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Principal Investigator |
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| Project Period (FY) |
2018-04-01 – 2021-03-31
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| Keywords | Activation function / LRT statistic / Regression analysis |
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| Outline of Final Research Achievements |
The success of the deep learning indicates its possible improvements in various ways. Improvements through the loss function and Bayesian models based on the likelihood ratio statistics are primary targets in the present study. The selection of activation functions, such as the softmax and the ReLU functions, is regarded as that of inferential procedures of parameters. The techniques of the estimation of a high-dimensional parameter are applied.
Two approaches are employed. One is to generalize activation functions by regarding them as ramp functions. The understanding of the ramp function varies with different disciplines, such as the spline function and the machine learning. We add a view of the heaviness of tail of the distribution. Another approach pertains the loss function. The loss and the risk are the keys in the deep learning, since it is broken down into the estimation problem of the multinomial distribution.
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| Free Research Field |
理論統計学・生物統計学
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| Academic Significance and Societal Importance of the Research Achievements |
データサイエンスへの期待が高まる中で、新し手法としての深層学習の実用性が認められた。その適用範囲は従来の統計手法が及ばない領域を広く含んでいる。また、その基本的構造は従来の回帰分析の自然な拡張である。その意味でも多様な研究が求められる研究テーマである。その構造の解明と理解を深める研究が求められている
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