Computational Algebraic Methods for Statistical Causal Inference

• Project/Area Number: 24700274
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Statistical science
• Research Institution: Seikei University (2014-2015); Tokyo Institute of Technology (2012-2013)
• Principal Investigator: Tanaka Kentaro 成蹊大学, 経済学部, 准教授 (00376948)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: 統計的因果推論 / 計算代数統計 / 条件付独立性 / 計算機代数統計 / 条件付き独立性 / 独立性 / アルゴリズム / 統計的推測 / 計算代数 / 統計数学

Outline of Final Research Achievements

Conditional independence is a fundamental concept in statistics and applied in a variety of fields. In order to analyze the properties of conditional independence, we deal with the implication problem of conditional independence statements, that is, testing whether a conditional independence statement is derived from a set of other conditional independence statements. In this research, we propose a new algebraic method for the implication problem among conditional independence statements, which is inspired by the factorization characterization of conditional independence.

Research Products

• [Int'l Joint Research] UTIA(チェコ)
• [Journal Article] カンファレンス行列と実験計画法 (2016)
  • Author(s): 田中研太郎
  • Journal Title: 品質 Volume: 46 Pages: 51-54
  • NAID: 110010041679
• [Journal Article] A linear-algebraic tool for conditional independence inference (2015)
  • Author(s): Kentaro Tanaka, Milan Studeny, A.Takemura and Tomonari Sei
  • Journal Title: Journal of Algebraic Statistics Volume: ６ Issue: 2 Pages: 150-167
  • DOI: 10.18409/jas.v6i2.46
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Cones of Elementary Imsets and Supermodular Functions: A Review and Some New Results (2012)
  • Author(s): Takuya Kashimura, Tomonari Sei, Akimichi Takemura and Kentaro Tanaka
  • Journal Title: Proceedings of the Second CREST-SBM International Conference "Harmony of Groebner Bases and the Modern Industrial Society" Volume: 0 Pages: 117-152
  • Peer Reviewed
• [Presentation] 実験計画法とGroup Lasso (2015)
  • Author(s): 田中研太郎
  • Organizer: 第27回 RAMP シンポジウム
  • Place of Presentation: 静岡大学 浜松キャンパス
  • Year and Date: 2015-10-15
  • Invited
• [Presentation] Linear algebraic methods and Groebner bases for experimental design and group lasso (2015)
  • Author(s): Kentaro Tanaka
  • Organizer: Current Trends on Groebner Bases
  • Place of Presentation: ホテル日航大阪
  • Year and Date: 2015-07-06
  • Int'l Joint Research
• [Presentation] Linear programming methods for conditional independence in- ference (2014)
  • Author(s): Kentaro Tanaka, Milan Studeny, Akimichi Takemura, Tomonari Sei
  • Organizer: Joint workshop on limit theorems and algebraic statistics
  • Place of Presentation: プラハ(チェコ)
  • Year and Date: 2014-08-25 – 2014-08-29
• [Presentation] Rules of Conditional Independence and Linear Algebra (2014)
  • Author(s): Kentaro Tanaka
  • Organizer: Workshop on Applications of Algebraic Geometry and Algebraic Analysis
  • Place of Presentation: 神戸大学
  • Year and Date: 2014-07-20 – 2014-07-21
• [Presentation] Linear Programming Methods for Conditional Independence Inference (2014)
  • Author(s): Kentaro TANAKA, Milan STUDENY, Akimichi TAKEMURA, Tomonari SEI
  • Organizer: Joint Workshop on LIMIT THEOREMS and ALGEBRAIC STATISTICS
  • Place of Presentation: プラハ（チェコ）
• [Presentation] Machine Learning Methods for Conditional Independence Inference (2013)
  • Author(s): Kentaro TANAKA, Milan STUDENY, Akimichi TAKEMURA, Tomonari SEI
  • Organizer: Tokyo satellite meeting of WSC2013
  • Place of Presentation: 東京
• [Presentation] Algebraic methods for conditional independence inference (2013)
  • Author(s): Kentaro TANAKA, Milan STUDENY, Akimichi TAKEMURA, Tomonari SEI
  • Organizer: 日本数学会2013年度秋季総合分科会
  • Place of Presentation: 愛媛
• [Presentation] A new method for Conditional Independence Inference (2012)
  • Author(s): Kentaro Tanaka
  • Organizer: The 9th Workshops on Uncertainty Processing
  • Place of Presentation: Czech Republic
• [Presentation] Optimization problems for intervention effects in structural equation models (2012)
  • Author(s): Kentaro Tanaka
  • Organizer: The 2nd Institute of Mathematical Statistics Asia Pacic Rim Meeting
  • Place of Presentation: Tsukuba, Japan
• [Remarks] tanaken-basis
  • URL: https://github.com/tanaken-basis/