Information geometry on deformed exponential probability distributions
| Project/Area Number |
17K05341
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Ibaraki University |
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Principal Investigator |
WADA Tatsuaki 茨城大学, 理工学研究科(工学野), 教授 (00240549)
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| Project Period (FY) |
2017-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
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| Keywords | 情報幾何学 / 変形指数型分布 / 共役表現 / 統計多様体 / 一般化エントロピ / 双対平坦 / エスコート分布 / エスコート期待値 / 情報幾何 / κ-指数型分布 |
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| Outline of Final Research Achievements |
It is well known that dually-flat structures are important geometric structures in Information geometry. In this research, we have studied the multiple dually-flat structures in information geometric structures of a general deformed-exponential family. We have found that i) the method to construct an appropriate statistical manifold from a general deformed-exponential family by using so-called "conjugate representation" proposed by J. Zhang; ii) characterizing escort-expectations by using our method; iii) the existing of the multiple dually-flat structures based on the multiple escort-expectations for a deformed-exponential family; iv) some applications to Thermodynamics, Statistical Physics, and related fields.
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| Academic Significance and Societal Importance of the Research Achievements |
従来の情報幾何において双対平坦性は非常に重要だが、それが多重に現れることはなかった。本研究の意義は、変形指数型分布の情報幾何構造において双対平坦性が多重に現れることを、多重エスコート期待値との関係により示したことにある。このメカニズムを、熱力学・統計力学における非平衡状態を記述する物理系へ適用することで、従来の指数型分布に対して成立する揺動散逸定理、揺動応答関係、揺らぎの定理などの熱系に対する重要な物理法則を、変形指数型分布に基づいて拡張する道が開かれ、情報幾何学のみならず、統計力学、統計推定、最適輸送などの様々な関連分野への波及効果があると期待できる。
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Report
(5 results)
Research Products
(24 results)
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[Journal Article] The κ-statistics approach to epidemiology2020
Author(s)
Kaniadakis Giorgio、Baldi Mauro M.、Deisboeck Thomas S.、Grisolia Giulia、Hristopulos Dionissios T.、Scarfone Antonio M.、Sparavigna Amelia、Wada Tatsuaki、Lucia Umberto
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Journal Title
Scientific Reports
Volume: 10
Issue: 1
Pages: 199949-199949
DOI
Related Report
Peer Reviewed / Open Access / Int'l Joint Research
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