High-dimensional semiparametric inference and machine learning

2018 Fiscal Year Final Research Report

• Project/Area Number: 15K00047
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Statistical science
• Research Institution: Chiba University (2018); Shimane University (2015-2017)
• Principal Investigator: Naito Kanta 千葉大学, 大学院理学研究院, 教授 (80304252)
• Research Collaborator: Yoshida Takuma ; Tamatani Mitsuru ; Notsu Akifumi
• Project Period (FY): 2015-04-01 – 2019-03-31
• Keywords: セミパラメトリック / 関数推定 / 高次元 / 機械学習

Outline of Final Research Achievements

Significant results have been obtained in each of three themes. In the theme "Pattern Recognition", asymptotic results for the naive canonical correlation coefficient have been developed, and a new statistical analysis based on the dilatation has been proposed. In the theme "Density Estimation", a robust version of local density estimation method has been proposed and its theoretical properties have been investigated. Furthermore, in the theme "Regression", an algorithm for regression based on the risk minimization has been considered and the performance of the resultant estimator has been clarified. Nonparametric kernel regression has been shown to work even in the setting where the explanatory variables are embedded into an unknown low dimensional manifold. A new method of nonlinear multivariate regression called the LMSR method has been proposed, and applied to analyze the development process of human fetuses.

Free Research Field

統計科学、数理統計学

Academic Significance and Societal Importance of the Research Achievements

学術的意義として、まず従来の統計解析手法をより広範なデータに適用可能とするための数理的拡張がなされた点が挙げられる。高次元データや外れ値を含むようなデータへの適用が可能となった。もう1点は、これまでになかった統計解析手法を構築した点である。特に、歪曲度を用いた多次元データの調和度解析や、多次元スタンダード曲線の構築法は、ヒト胎児の発生過程の解析を念頭に考案された。本研究で新たに考案されたこれらの手法により、ヒト胎児の臓器の発生について様々な知見を得ることができた点は、社会的意義となる。