论文标题
概率单纯性和广义组成数据上的参数谎言组结构
Parametric Lie group structures on the probabilistic simplex and generalized Compositional Data
论文作者
论文摘要
在本文中，我们在概率的单纯形上构建了一组参数商的谎言组结构，可以扩展到实际矢量空间结构。特别是，我们重新发现了将组合数据作为与标准不变性原理引起的等效关系相关的元素相关的元素时通常使用的主要数学对象。这种观点有助于适应用于经典组成数据的统计方法，以遵循更一般的对等关系。
In this paper we build a set of parametric quotient Lie group structures on the probabilistic simplex that can be extended to real vector space structures. In particular, we rediscover the main mathematical objects generally used when treating compositional data as elements associated to the quotient Lie group with respect to the equivalence relation induced by the scale invariance principle. This perspective facilitates the adaptation of the statistical methods used for classical compositional data to data that follows a more general equivalence relation.
