具有复曲面结构的阶段树模型
Staged tree models with toric structure
摘要：
阶段树模型是一种离散的统计模型，对事件之间的关系进行编码。这些模型是由带有着色顶点的有向树实现的。在代数几何术语中，模型由复曲面簇内的点组成。对于某些称为平衡树的树，模型实际上是复曲面簇和概率单形的交集。这给了模型一个简单的描述，并具有计算优势。在本文中，我们表明，类的阶段树模型与复曲面结构的平衡情况下，如果我们允许改变的坐标延伸远远超出。是否所有的阶段树模型都具有环面结构是一个悬而未决的问题。
英文摘要：
A staged tree model is a discrete statistical model encoding relationships between events. These models are realised by directed trees with coloured vertices. In algebro-geometric terms, the model consists of points inside a toric variety. For certain trees, called balanced, the model is in fact the intersection of the toric variety and the probability simplex. This gives the model a straightforward description, and has computational advantages. In this paper we show that the class of staged tree models with a toric structure extends far outside of the balanced case, if we allow a change of coordinates. It is an open problem whether all staged tree models have toric structure.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
