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

Research Project

Project/Area Number 19K24340
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeMulti-year Fund
Review Section 1001:Information science, computer engineering, and related fields
Research InstitutionTokyo 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
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords統計モデリング / 非凸性 / 推定アルゴリズム / 実データ解析 / 非凸最適化 / 収束保証
Outline of Research at the Start

本研究の目的は,実データの諸問題に対応しようとすると自然と現れる非凸性に基づく統計モデリングを対象とし,そのパラメータ推定のための非凸最適化アルゴリズムに対して,収束保証を与えることである.既存の非凸最適化アルゴリズムの,理論的な適用範囲を拡張を行うだけでなく,統計モデリングの段階でアルゴリズムと親和性の高いモデリングを考えることで,統計モデリングと最適化両者の良さを打ち消すことなくデータ解析を行う統計モデリングを可能にしたい.

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.

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。

Report

(5 results)
  • 2022 Annual Research Report   Final Research Report ( PDF )
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • Research Products

    (8 results)

All 2022 2021 2020 2019

All Journal Article (5 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 5 results,  Open Access: 3 results) Presentation (3 results) (of which Invited: 3 results)

  • [Journal Article] Robust regression against heavy heterogeneous contamination2022

    • Author(s)
      Kawashima Takayuki、Fujisawa Hironori
    • Journal Title

      Metrika

      Volume: 86 Issue: 4 Pages: 421-442

    • DOI

      10.1007/s00184-022-00874-1

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Public transportation network scan for rapid surveillance2022

    • Author(s)
      Tanoue Yuta、Yoneoka Daisuke、Kawashima Takayuki、Uryu Shinya、Nomura Shuhei、Eguchi Akifumi、Makiyama Koji、Matsuura Kentaro
    • Journal Title

      Biostatistics & Epidemiology

      Volume: - Issue: 1 Pages: 1-15

    • DOI

      10.1080/24709360.2022.2065628

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Distributed lag interrupted time series model for unclear intervention timing: effect of a statement of emergency during COVID-19 pandemic2022

    • Author(s)
      Yoneoka Daisuke、Kawashima Takayuki、Tanoue Yuta、Nomura Shuhei、Eguchi Akifumi
    • Journal Title

      BMC Medical Research Methodology

      Volume: 22 Issue: 1

    • DOI

      10.1186/s12874-022-01662-1

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Geographically weighted generalized Farrington algorithm for rapid outbreak detection over short data accumulation periods2021

    • Author(s)
      Yoneoka Daisuke、Kawashima Takayuki、Makiyama Koji、Tanoue Yuta、Nomura Shuhei、Eguchi Akifumi
    • Journal Title

      Statistics in Medicine

      Volume: 40 Issue: 28 Pages: 6277-6294

    • DOI

      10.1002/sim.9182

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] EM algorithm using overparameterization for the multivariate skew-normal distribution2021

    • Author(s)
      Abe Toshihiro、Fujisawa Hironori、Kawashima Takayuki、Ley Christophe
    • Journal Title

      Econometrics and Statistics

      Volume: 19 Pages: 151-168

    • DOI

      10.1016/j.ecosta.2021.03.003

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] 射影勾配法による高次元回帰モデリング2020

    • Author(s)
      川島孝行
    • Organizer
      2020年度科研費シンポジウム 「多様な分野のデータに対する統計科学・機械学習的アプローチ」
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] ロバストかつスパースな回帰モデリング2019

    • Author(s)
      川島 孝行
    • Organizer
      第4回統計・機械学習若手シンポジウム
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] ガンマ・ダイバージェンス最小化に基づくロバストかつスパースな回帰2019

    • Author(s)
      川島 孝行
    • Organizer
      統計学と機械学習の数理と展開
    • Related Report
      2019 Research-status Report
    • Invited

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Published: 2019-09-03   Modified: 2024-01-30  

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