论文标题
群体素的信息几何形状：奇异指标的情况
Information geometry on groupoids: the case of singular metrics
论文作者
论文摘要
我们将一般设置用于lie groupoid和lie代数提供的统计和信息几何形状中的对比度（潜在）函数。对比函数是在lie grassoid上定义的，并在相应的Lie代数上产生两种形式和三种形式。我们研究了两种形式退化的情况，并显示在足够规则的情况下如何将其降低到假学结构。 Riemannian叶子的横向LEVI-CIVITA连接被推广到lie groupoid/lie代数案例。
We use the general setting for contrast (potential) functions in statistical and information geometry provided by Lie groupoids and Lie algebroids. The contrast functions are defined on Lie groupoids and give rise to two-forms and three-forms on the corresponding Lie algebroid. We study the case when the two-form is degenerate and show how in sufficiently regular cases one reduces it to a pseudometric structures. Transversal Levi-Civita connections for Riemannian foliations are generalized to the Lie groupoid/Lie algebroid case.
