Many questions in science center around the fundamental problem of understanding causal relationships. However, most constraint-based causal discovery algorithms, including the well-celebrated PC algorithm, often incur an exponential number of conditional independence (CI) tests, posing limitations in various applications. Addressing this, our work focuses on characterizing what can be learned about the underlying causal graph with a reduced number of CI tests. We show that it is possible to a learn a coarser representation of the hidden causal graph with a polynomial number of tests. This coarser representation, named Causal Consistent Partition Graph (CCPG), comprises of a partition of the vertices and a directed graph defined over its components. CCPG satisfies consistency of orientations and additional constraints which favor finer partitions. Furthermore, it reduces to the underlying causal graph when the causal graph is identifiable. As a consequence, our results offer the first efficient algorithm for recovering the true causal graph with a polynomial number of tests, in special cases where the causal graph is fully identifiable through observational data and potentially additional interventions.

翻译：科学中的许多问题都围绕着理解因果关系的根本问题展开。然而，大多数基于约束的因果发现算法，包括备受推崇的PC算法，通常需要进行指数级数量的条件独立性检验，这在各种应用中带来了局限性。针对这一问题，我们的工作重点在于刻画：通过减少条件独立性检验的数量，能够从潜在的因果图中学习到什么。我们证明，通过多项式次数的检验，可以学习到隐藏因果图的一种更粗略的表示。这种更粗略的表示被称为因果一致划分图，它由顶点的一个划分以及在其分量上定义的一个有向图组成。CCPG满足方向的一致性以及倾向于更细划分的额外约束。此外，当因果图可识别时，它会简化为潜在的因果图。因此，我们的研究结果首次提供了一种高效的算法，能够在因果图完全可以通过观测数据（以及可能额外的干预）识别的特殊情况下，通过多项式次数的检验来恢复真实的因果图。