Information Geometry Associated with Generalized Means
Information Geometry Associated with Generalized Means
复制标题
与广义均值相关的信息几何
DOI：
10.1007/978-3-319-97798-0_10
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Osamu Komori and Atsumi Ohara
中科院分区：
文献类型：
--
作者：
Shinto Eguchi;Osamu Komori and Atsumi Ohara
本文旨在为信息几何的标准框架提供自然的扩展。主要思想是定义e-测地线和m-测地线的概括，它与规范散度和广义期望相关联。广义电子测地线由 Kolmogorov-Nagumo 方法给出；广义 m 测地线的特征是保留广义期望。关于正则散度的毕达哥拉斯定理在采用广义 e 测地线和 m 测地线的所有概率密度函数的空间中示出。因此，我们为标准框架提供了广泛的概括，其中仍然存在与标准框架类似的与两个广义测地线相关的二元结构。
This paper aims to provide a natural extension for the standard framework of information geometry. The main idea is to define a generalization of e-geodesic and m-geodesic, which associates with the canonical divergence and generalized expectation. The generalized e-geodesic is given by Kolmogorov–Nagumo means; the generalized m-geodesic is characterized to preserve the generalized expectation. The Pythagorean theorem with respect to the canonical divergence is shown in the space of all probability density functions employing the generalized e-geodesic and m-geodesic. As a result, we provide a wide class of generalization for the standard framework, in which there is still a dualistic structure associated with the two generalized geodesics as similar to the standard framework.