Dimensional reduction method with interpretable estimated values

2021 Fiscal Year Final Research Report

• Project/Area Number: 19K20226
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 60030:Statistical science-related
• Research Institution: Doshisha University (2021); Tokyo University of Science (2019-2020)
• Principal Investigator: Tsuchida Jun 同志社大学, 文化情報学部, 助教 (40828365)
• Project Period (FY): 2019-04-01 – 2022-03-31
• Keywords: 主成分分析 / 因子分析 / 因子回転法 / 交互最小2乗法

Outline of Final Research Achievements

In this study, we used the Gini Index to measure the interpretability of estimated values. We developed dimensional reduction methods with the constraint that the Gini Index must be above a particular value. From this constraint, we could obtain the sparse estimated values with a large variance. This characteristic of the estimated values corresponds to the interpretability.
We have developed two methods: One is principal component analysis with the constraint that the Gini Index must be above a certain level. The other is a rotation method for factor analysis. We reported the study results to the public through conference presentations.

Free Research Field

統計科学

Academic Significance and Societal Importance of the Research Achievements

“解釈容易性”の議論は実用上重要であるが，現在，積極的に議論されていない．本研究では，Thurston(1947) が言葉でのみ定義した解釈容易性を，式によって表現することを目標とした．解釈容易性を式によって表現することで，実用上重要な問題である“解釈容易性”を担保した新しい統計手法の構築の基礎を作ることができる．本研究ではGini Index を用いて解釈容易性が定義できるかを検証し，解釈容易性を最大化する次元縮約法を開発した．本研究の成果は，新しい統計手法の構築の基礎の一助となる．