Non-Commutative Extension of the Information Geometry
Non-Commutative Extension of the Information Geometry
复制标题
信息几何的非交换扩展
DOI：
10.1007/978-1-4899-1391-3_31
复制
发表时间：
1995
影响因子：
0.8
通讯作者：
H. Hasegawa
中科院分区：
文献类型：
--
作者：
H. Hasegawa
结果表明，Amari 构建的关于经典概率参数空间中光滑流形结构的统计微分几何公式 S = {p(·, θ)| 可以扩展到非交换框架，至少在有限维代数内，其中经典概率 p(·, θ) 被密度矩阵 ρ(θ) 代替。简要概述了该框架，重点是阐明所谓的 ρ 的 α 族的显着二元结构，特别是在 |α|= 1 的情况下（即 log ρ 和 ρ 之间的二元结构）。
It is shown that the differential-geometrical formulation of statistics concerning the structure of a smooth manifold in the parameter space of classical probabilities, S = {p(·, θ)|, which was constructed by Amari can be extended to the non-commutative framework, at least, within finite dimensional algebras where the classical probabilities p(·, θ) are replaced by density matrices, ρ(θ). A brief outline of the framework is presented with the emphasis on elucidating the remarkable dualistic structure of the so-called α-families of ρ′s,specifically, in the case of |α|= 1 (i.e. the dualistic structure between log ρ and ρ).