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.

ID 算法在图形因果模型中解决了识别干预分布 p (Y | do (a)) 的问题，并且已经以多种方式进行了表述。然而文献中提出的 'hedge criterion'（第 3 个推论）作为 ID 算法无法识别输入的图形特征是错误的，本文概述了 ID 算法的现代演示，讨论了反例的简单例子，并提供了一些 ID 算法无法识别其输入分布的图形特征。

ID 算法在什么时候会失败？

When does the ID algorithm fail?

We prove the main rules of causal calculus (also called do-calculus) for i/o
structural causal models (ioSCMs), a generalization of a recently proposed
general class of non-/linear structural causal models that allow for cycles,
latent confounders and arbitrary probability distributions. We also generalize
adjustment criteria and formulas from the acyclic setting to the general one
(i.e. ioSCMs). Such criteria then allow to estimate (conditional) causal
effects from observational data that was (partially) gathered under selection
bias and cycles. This generalizes the backdoor criterion, the
selection-backdoor criterion and extensions of these to arbitrary ioSCMs.
Together, our results thus enable causal reasoning in the presence of cycles,
latent confounders and selection bias. Finally, we extend the ID algorithm for
the identification of causal effects to ioSCMs.

该研究证明了 IOSCM 模型中的因果推理原则，包括调整标准和公式，从而使得能够在具有循环、潜在的混杂变量和选择偏差的情况下估算出条件因果效应，并扩展了 ID 算法以在这些模型中进行因果效应的识别。