论文标题
在Banach空间上建模的双重仿射信息几何形状
Dually affine Information Geometry modeled on a Banach space
论文作者
论文摘要
在本章中，我们从特定的非参数或功能的角度研究信息几何形状。基本模型是通常由规律条件指定的概率子集。例如，概率以给定的平滑度度量相互绝对连续或概率密度。我们通过将图表的图表作为从概率到Banach空间的映射来构建多种结构。我们使用的图表非常奇特，因为我们仅考虑过渡映射是仿射的实例。我们在此仿射环境中选择了切线和cotangent束的特殊表达。
In this chapter, we study Information Geometry from a particular non-parametric or functional point of view. The basic model is a probabilities subset usually specified by regularity conditions. For example, probability measures mutually absolutely continuous or probability densities with a given degree of smoothness. We construct a manifold structure by giving an atlas of charts as mappings from probabilities to a Banach space. The charts we use are quite peculiar in that we consider only instances where the transition mappings are affine. We chose a particular expression of the tangent and cotangent bundles in this affine setting.
