论文标题
离散介入模型的代数几何形状
Algebraic geometry of discrete interventional models
论文作者
论文摘要
我们研究了离散DAG模型中一般干预措施的代数和几何形状。为此，我们介绍了一种在较为一般的阶段树模型家族中建模软干预措施的理论，并开发了形式主义，将这些模型作为概率简单产物的参数性亚变化进行研究。然后，我们考虑找到其定义方程式的问题，并得出了一个组合标准，用于识别介入的介绍树模型，其定义理想是复形的。我们将这些结果应用于离散介入的DAG模型的类别，并建立标准以确定这些模型何时是折叠品种。
We investigate the algebra and geometry of general interventions in discrete DAG models. To this end, we introduce a theory for modeling soft interventions in the more general family of staged tree models and develop the formalism to study these models as parametrized subvarieties of a product of probability simplices. We then consider the problem of finding their defining equations, and we derive a combinatorial criterion for identifying interventional staged tree models for which the defining ideal is toric. We apply these results to the class of discrete interventional DAG models and establish a criteria to determine when these models are toric varieties.
