Evaluating graphs learned by causal discovery algorithms is difficult: The
number of edges that differ between two graphs does not reflect how the graphs
differ with respect to the identifying formulas they suggest for causal
effects. We introduce a framework for developing causal distances between
graphs which includes the structural intervention distance for directed acyclic
graphs as a special case. We use this framework to develop improved
adjustment-based distances as well as extensions to completed partially
directed acyclic graphs and causal orders. We develop polynomial-time
reachability algorithms to compute the distances efficiently. In our package
gadjid (open source at this https URL), we provide
implementations of our distances; they are orders of magnitude faster than the
structural intervention distance and thereby provide a success metric for
causal discovery that scales to graph sizes that were previously prohibitive.

评估因果发现算法学习到的图形是困难的：两个图形之间不同的边的数量不反映它们在提供因果效应的标识公式方面的差异。我们介绍了一种开发图形之间因果距离的框架，其中包括有向无环图的结构干预距离作为一种特殊情况。我们利用这个框架开发了改进的基于调整的距离以及对已完成的部分有向无环图和因果顺序的扩展。我们开发了多项式时间可达性算法以高效地计算距离。在我们的包 gadjid（开源网址如上所示），我们提供了距离的实现；它们的速度比结构干预距离快几个数量级，从而为可扩展到以前禁止的图形规模的因果发现提供了成功度量。