论文标题
通过行安排和点配置的条件概率
Conditional probabilities via line arrangements and point configurations
论文作者
论文摘要
我们研究了满足某些条件独立性（CI）约束的概率分布之间的联系，以及入射率几何形状中的点和线排列。对于一个CI陈述的家族，我们将代数不变性的多项式理想与多项式相关联。这些理想的主要分解给出了满足原始CI语句的分布的特征。从经典上讲，这些理想是由变量矩阵的2分钟产生的，但是，在存在隐藏变量的情况下，它们包含更高程度的未成年人。这导致研究了确定性超图理想的结构，这些理想的分解可以从投影空间中的点和线构型来理解。
We study the connection between probability distributions satisfying certain conditional independence (CI) constraints, and point and line arrangements in incidence geometry. To a family of CI statements, we associate a polynomial ideal whose algebraic invariants are encoded in a hypergraph. The primary decompositions of these ideals give a characterisation of the distributions satisfying the original CI statements. Classically, these ideals are generated by 2-minors of a matrix of variables, however, in the presence of hidden variables, they contain higher degree minors. This leads to the study of the structure of determinantal hypergraph ideals whose decompositions can be understood in terms of point and line configurations in the projective space.
