主催: 横断型基幹科学技術研究団体連合
会議名: 第10回横幹連合コンファレンス
回次: 10
開催地: 新潟県長岡市 長岡技術科学大学
開催日: 2019/11/30 - 2019/12/01
Information Geometry has been advocated by Shun-ichi Amari in early 1980s, which provides a geometric insight for understanding statistical ideas such as information, sufficiency and efficiency. Furthermore, it is closely connected with almost all of areas in mathematical sciences including information, statistical, physical, biological and brain sciences. One of the most characteristic of information geometry is in a dualistic pair of e-connection and m-connection in the space of all probability density functions, which can be viewed as a Riemannian space with a metric tensor derived by the Fisher information matrix. Surprisingly, the essential theorem can reduce to the Pythagorean theorem developed in the ancient Greek era, which provides a view for the interplay between a statistical model and estimation expanding a Pythagorean foliation in the probability density function space. Finally, we have a review for the present address and future directions in information geometry.