オハラ　アツミ   Atsumi Ohara   小原　敦美    所属   追手門学院大学  理工学部 数理・データサイエンス学科    職種   教授
言語種別	英語
発行・発表の年月	2017
形態種別	論文
査読	査読あり
標題	On affine immersions of the probability simplex and their conformal flattening
執筆形態	単著
掲載誌名	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
掲載区分	国外
出版社・発行元	Springer Verlag
巻・号・頁	10589,pp.247-254
著者・共著者	Atsumi Ohara
概要	Embedding or representing functions play important roles in order to produce various information geometric structure. This paper investigates them from a viewpoint of affine differential geometry [2]. By restricting affine immersions to a certain class, the probability simplex is realized to be 1-conformally flat [3] statistical manifolds immersed in Rn+1. Using this fact, we introduce a concept of conformal flattening of such manifolds to obtain dually flat statistical (Hessian) ones with conformal divergences, and show explicit forms of potential functions, dual coordinates. Finally, we demonstrate applications of the conformal flattening to nonextensive statistical physics and certain replicator equations on the probability simplex.
DOI	10.1007/978-3-319-68445-1_29
ISSN	1611-3349