An extension to multi-fused criterion for Renyi divergence and its application to apportionment

2020 Fiscal Year Final Research Report

• Project/Area Number: 18K03413
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 12040:Applied mathematics and statistics-related
• Research Institution: Osaka University
• Principal Investigator: Hamada Etsuo 大阪大学, 基礎工学研究科, 特任教授(常勤) (20273617)
• Project Period (FY): 2018-04-01 – 2021-03-31
• Keywords: ダイバージェンス / モデル評価基準 / ロバストネス

Outline of Final Research Achievements

In response to this research, we derived a divergence family of criteria that generalizes AIC by a robust generalization of the model selection criterion family, showed that this family is asymptotically equivalent to AIC in polynomial regression models, and further showed that it performs well even in the presence of outliers. Based on these results, we proposed a new information criterion, RCC, which is based on the influence function, as a robust information criterion for analyzing data with outliers using polynomial regression models, and which has both the consistency corresponding to BIC and the robustness corresponding to BHHJ.

Free Research Field

数理統計学

Academic Significance and Societal Importance of the Research Achievements

モデル選択基準族において、外れ値を持つデータに対しても十分有効なパフォーマンスを発揮する情報量規準の提案が望まれていたが、この研究成果では多項式回帰モデルという制限下ではあるが、一致性と頑健性を併せ持つ新しい情報量規準 RCC を提案することが出来たのは、大きな学術的意義を持つと同時に、データサイエンスの現場での応用可能という意味で社会的意義を持つといえる。