论文标题
结构统计的应用：指数家族的几何推断
Applications of Structural Statistics: Geometric Inference in Exponential Families
论文作者
论文摘要
指数家庭包括广泛的统计模型和参数族，例如正常分布，二项式分布，伽马分布或指数分布。因此，其概率分布的形式表示会引起狭窄的内在结构，这似乎是双重平坦的统计歧管。相反，可以证明，任何双重平坦的统计流形，这是由常规的布雷格曼（Bregman）差异唯一引起的定期指数家族给出的，因此指数式的家庭可以（有些限制）被视为双重平坦统计流形的普遍表示。本文回顾了Shun'ichi Amari的开创性工作，内容涉及指数家庭在结构层面上的内在结构。
Exponential families comprise a broad class of statistical models and parametric families like normal distributions, binomial distributions, gamma distributions or exponential distributions. Thereby the formal representation of its probability distributions induces a confined intrinsic structure, which appears to be that of a dually flat statistical manifold. Conversely it can be shown, that any dually flat statistical manifold, which is given by a regular Bregman divergence uniquely induced a regular exponential family, such that exponential families may - with some restrictions - be regarded as a universal representation of dually flat statistical manifolds. This article reviews the pioneering work of Shun'ichi Amari about the intrinsic structure of exponential families in terms of structural stratistics.
