Peters Jonas, Bühlmann Peter
Seminar for Statistics, Department of Mathematics, ETH Zürich 8092, Switzerland
Neural Comput. 2015 Mar;27(3):771-99. doi: 10.1162/NECO_a_00708. Epub 2015 Jan 20.
Causal inference relies on the structure of a graph, often a directed acyclic graph (DAG). Different graphs may result in different causal inference statements and different intervention distributions. To quantify such differences, we propose a (pre-)metric between DAGs, the structural intervention distance (SID). The SID is based on a graphical criterion only and quantifies the closeness between two DAGs in terms of their corresponding causal inference statements. It is therefore well suited for evaluating graphs that are used for computing interventions. Instead of DAGs, it is also possible to compare CPDAGs, completed partially DAGs that represent Markov equivalence classes. The SID differs significantly from the widely used structural Hamming distance and therefore constitutes a valuable additional measure. We discuss properties of this distance and provide a (reasonably) efficient implementation with software code available on the first author's home page.
因果推断依赖于图的结构，通常是有向无环图（DAG）。不同的图可能会导致不同的因果推断陈述和不同的干预分布。为了量化这些差异，我们提出了一种DAG之间的（预）度量——结构干预距离（SID）。SID仅基于图形标准，并根据两个DAG相应的因果推断陈述来量化它们之间的接近程度。因此，它非常适合评估用于计算干预的图。除了DAG之外，也可以比较CPDAG，即表示马尔可夫等价类的部分完成的DAG。SID与广泛使用的结构汉明距离有显著差异，因此构成了一种有价值的附加度量。我们讨论了这种距离的性质，并在第一作者的主页上提供了带有软件代码的（合理）高效实现。
