Unified construction of geometric theory for information space and morphological information science

2019 Fiscal Year Final Research Report

• Project/Area Number: 16KT0132
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 特設分野
• Research Field: Mathematical Sciences in Search of New Cooperation
• Research Institution: Nagoya Institute of Technology
• Principal Investigator: Matsuzoe Hiroshi 名古屋工業大学, 工学(系)研究科(研究院), 教授 (90315177)
• Co-Investigator(Kenkyū-buntansha): 高津 飛鳥 首都大学東京, 理学研究科, 准教授 (90623554)
• Project Period (FY): 2016-07-19 – 2020-03-31
• Keywords: 情報幾何学 / マルコフ埋め込み

Outline of Final Research Achievements

In information geometry, the invariance of geometric structures for statistical models under Markov embedding is very important. However, our research group found that the construction of Markov embedding is not unique, and the embedding can be modified. As a result, it is shown that different invariants corresponding to the new Markov embedding are obtained.
The result of this study, which was not expected at the beginning of this research project, is an important development on the basic properties of information geometry.

Free Research Field

幾何学

Academic Significance and Societal Importance of the Research Achievements

情報幾何学における不変性の要請は，情報空間の幾何学構成において非常に重要な基本原則である．しかしながら，その不変性に任意性があり，従来とは異なる自然な埋め込みを構成することで，新しい幾何学構造の不変性が得られることを示した．この研究成果は情報空間の微分幾何学的基礎理論として，非常に重要であると考えている．