Finding a directed acyclic graph (DAG) that best encodes the conditional independence statements observable from data is a central question within causality. Algorithms that greedily transform one candidate DAG into another given a fixed set of moves have been particularly successful, for example the GES, GIES, and MMHC algorithms. In 2010, Studen\'y, Hemmecke and Lindner introduced the characteristic imset polytope, $\textrm{CIM}_p$, whose vertices correspond to Markov equivalence classes, as a way of transforming causal discovery into a linear optimization problem. We show that the moves of the aforementioned algorithms are included within classes of edges of $\textrm{CIM}_p$ and that restrictions placed on the skeleton of the candidate DAGs correspond to faces of $\textrm{CIM}_p$. Thus, we observe that GES, GIES, and MMHC all have geometric realizations as greedy edge-walks along $\textrm{CIM}_p$. Furthermore, the identified edges of $\textrm{CIM}_p$ strictly generalize the moves of these algorithms. Exploiting this generalization, we introduce a greedy simplex-type algorithm called greedy CIM, and a hybrid variant, skeletal greedy CIM, that outperforms current competitors among hybrid and constraint-based algorithms.
翻译:找到一个直接的自行车图( DAG ), 将从数据中观察到的有条件的独立声明编码为最佳, 是因果关系的一个中心问题。 将一个候选的 DAG 贪婪地转换成另一个选择的DAG, 并且有一套固定的动作, 尤其成功, 例如 GES、 GIES 和 MMHC 算法 。 2010年, Studen\'y、 Hemmecke 和 Lindner 引入了典型的隐含聚点、 $\ textrm{ CIM ⁇ p$, 其顶端与 Markov 等值等级相对应, 作为将因果关系发现转化为线性优化问题的一种方法。 我们显示, 上述算法的动作包含在 $\ textrm{ CIM ⁇ p$ 的边缘, 对候选人 DAGS的骨架设置的限制与 $\ textrm{ CIM ⁇ p$ 相匹配。 因此, 我们观察到, GES、 GDE 和MHC- divilalalalalalalal- dalizalalalization exalizalization 。