Characteristic imsets are 0/1-vectors representing directed acyclic graphs whose edges represent direct cause-effect relations between jointly distributed random variables. A characteristic imset (CIM) polytope is the convex hull of a collection of characteristic imsets. CIM polytopes arise as feasible regions of a linear programming approach to the problem of causal disovery, which aims to infer a cause-effect structure from data. Linear optimization methods typically require a hyperplane representation of the feasible region, which has proven difficult to compute for CIM polytopes despite continued efforts. We solve this problem for CIM polytopes that are the convex hull of imsets associated to DAGs whose underlying graph of adjacencies is a tree. Our methods use the theory of toric fiber products as well as the novel notion of interventional CIM polytopes. Our solution is obtained as a corollary of a more general result for interventional CIM polytopes. The identified hyperplanes are applied to yield a linear optimization-based causal discovery algorithm for learning polytree causal networks from a combination of observational and interventional data.

翻译：特征imset是表示有向无环图的0/1向量，其边表示联合分布随机变量之间的直接因果关系。特征imset（CIM）多面体是一组特征imset的凸包。CIM多面体作为因果发现问题的线性规划方法的可行域出现，该问题旨在从数据中推断因果结构。线性优化方法通常需要可行域的超平面表示，尽管持续努力，但计算CIM多面体的超平面表示一直存在困难。我们针对底层邻接图为树的DAG所关联的imset的凸包构成的CIM多面体解决了这一问题。我们的方法利用环面纤维积理论以及干预CIM多面体的新概念。我们的解是作为干预CIM多面体更一般结果的推论而获得的。所识别的超平面被应用于产生一种基于线性优化的因果发现算法，用于从观测数据和干预数据的组合中学习多树因果网络。