离散干预模型的代数几何
Algebraic geometry of discrete interventional models
AI总结：
本文研究离散DAG模型中一般干预的代数几何，引入分段树模型理论，推导出定义理想为环面的组合判据，并应用于离散干预DAG模型以确定其环面簇性质。
摘要：
我们研究了离散有向无环图模型中一般干预的代数与几何性质。为此，我们引入了一种在更一般的分段树模型族中对软干预进行建模的理论，并发展了将这些模型视为概率单纯形乘积的参数化子簇的形式体系。随后，我们考虑了寻找其定义方程的问题，并推导出一个组合判据，用于识别定义理想为环面的干预分段树模型。我们将这些结果应用于离散干预有向无环图模型类，并建立了确定这些模型何时为环面簇的判据。
英文摘要：
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.
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。
