The ID algorithm solves the problem of identification of interventional distributions of the form p(Y | do(a)) in graphical causal models, and has been formulated in a number of ways [12, 9, 6]. The ID algorithm is sound (outputs the correct functional of the observed data distribution whenever p(Y | do(a)) is identified in the causal model represented by the input graph), and complete (explicitly flags as a failure any input p(Y | do(a)) whenever this distribution is not identified in the causal model represented by the input graph). The reference [9] provides a result, the so called "hedge criterion" (Corollary 3), which aims to give a graphical characterization of situations when the ID algorithm fails to identify its input in terms of a structure in the input graph called the hedge. While the ID algorithm is, indeed, a sound and complete algorithm, and the hedge structure does arise whenever the input distribution is not identified, Corollary 3 presented in [9] is incorrect as stated. In this note, I outline the modern presentation of the ID algorithm, discuss a simple counterexample to Corollary 3, and provide a number of graphical characterizations of the ID algorithm failing to identify its input distribution.

翻译：ID算法解决了图形因果模型中形如 p(Y | do(a)) 的干预分布识别问题，并已通过多种方式进行了公式化表述[12, 9, 6]。该算法是可靠的（当输入图形所表示的因果模型中 p(Y | do(a)) 可识别时，能输出观测数据分布的正确函数），且是完备的（当输入分布 p(Y | do(a)) 在输入图形表示的因果模型中不可识别时，会明确标记失败）。文献[9]提出了一个称为“篱笆准则”的结果（推论3），旨在基于输入图中名为“篱笆”的结构，给出ID算法识别失败情形的一种图形刻画。尽管ID算法确实是一种可靠且完备的算法，且当输入分布不可识别时总会产生篱笆结构，但文献[9]中提出的推论3在表述上是不正确的。本文概述了ID算法的现代表述方式，讨论了推论3的一个简单反例，并提供了ID算法识别输入分布失败时的若干种图形刻画。