Statistical modeling based on non-convexity with convergence guaranteed estimation algorithm

2022 Fiscal Year Final Research Report

• Project/Area Number: 19K24340
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Multi-year Fund
• Review Section: 1001:Information science, computer engineering, and related fields
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: Kawashima Takayuki 東京工業大学, 情報理工学院, 助教 (60846210)
• Project Period (FY): 2019-08-30 – 2023-03-31
• Keywords: 統計モデリング / 非凸性 / 推定アルゴリズム

Outline of Final Research Achievements

We study statistical modeling based on the non-convexity that naturally arises when dealing with problems in real data analysis. The research aimed to simultaneously achieve not only statistical properties but also efficiency of the estimation algorithm.
i) In a study of estimation algorithms for skew-normal distributions, we succeeded in deriving an update formula that naturally includes an momentum term that generally accelerates estimation. Numerical experiments have shown that our estimation algorithm can perform in less computation time compared with conventional estimation algorithms.
ii) We have incorporated a geographically weighted regression model into the farrington algorithm used in excess mortality. It allows inferences to be made even with small amounts of data.

Free Research Field

統計科学

Academic Significance and Societal Importance of the Research Achievements

歪正規分布はそのモデリングの柔軟性から広い分野ですでに使われており、今回の研究により短時間での推定が可能になったため、より大規模なデータにも適用可能である。
超過死亡推定のために用いられているFarringtonアルゴリズムを少ないデータでも推定できるように拡張を行ったことで、データを大量に習得ができない状況や、対象の事象が初期の段階でも、本アルゴリズムを適用することで推定が可能になった。