Development of model evaluation criteria based on statistical divergence and evaluation for criteria

2023 Fiscal Year Final Research Report

• Project/Area Number: 20K19753
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 60030:Statistical science-related
• Research Institution: Kyushu University (2022-2023); The University of Tokyo (2020-2021)
• Principal Investigator: Kurata Sumito 九州大学, マス・フォア・インダストリ研究所, 助教 (10847122)
• Project Period (FY): 2020-04-01 – 2024-03-31
• Keywords: モデル選択 / 統計的ダイバージェンス / ロバストネス / 漸近理論 / ベイズ統計学 / スパースモデリング / 食品科学 / 地球科学

Outline of Final Research Achievements

In real data, there frequently exist some outliers (observations that are markedly different in value from others) derived from, for example, unusual abilities, catastrophe-level phenomena, or human errors. It is difficult to provide a clear definition or threshold of such outliers, moreover, it is effectively impossible to prevent their occurrence, thus, robust methods that reduce the influence of outliers are significantly important. In this study, I investigated a model selection methods that are robust against outliers. By utilizing statistical divergence, a measure of remoteness between probability distributions, I measured the "farness" between the model and the underlying "true distribution", and derived a model that can adequately represent a phenomenon or behavior. Additionally, I theoretically evaluated the performance of the selection method.

Free Research Field

数理統計学、モデル選択、ロバストネス

Academic Significance and Societal Importance of the Research Achievements

あらゆる分野にデータは存在し、必然的にモデルが構築できる以上、「良きモデル」を択ぶ「良き規準」の開発は文理を問わない広い分野に対し意義を持つ。本研究は、導出に於ける理論的正当性や多様な設定に対する運用可能性に加えて、頑健性を中心とした規準の「良さ」を定式化し、理論的・数値実験的な比較を行うことに力点を置いた。「規準の良さ」についての考察を行い、多様な場面・設定下で、「評価規準を評価する為の規準」を構築することにより、数多存在する規準の長短や、それらの適切な使い道を示し、幅広い設定に対応した手法を開発・評価することで、諸分野の「良い」結論の妥当性ある保証を目指した。