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.

This paper focuses on the application of one type of empirical methods, namely statistical causal inference (SCI, see section 2). Such methods have their roots in a number of applied fields (from AI to econometrics) and aim to provide a framework for making valid inferences about causal effects based on interventional or observational data. More specifically, we focus on SCI methods that use graphical models as developed by Pearl and colleagues [1, 2]. This framework has been shown to be equivalent of the potential-outcomes framework (also called the Neyman-Rubin Causal Model [3]) but enriches it by making use of an explicit causal structure called a graphical causal model. Making assumptions about causal effects explicit through a graphical structure has several advantages. First, it helps determine whether causal effects can be estimated and how they might be estimated (see section 2).

We introduce DoWhy-GCM, an extension of the DoWhy Python library, that leverages graphical causal models. Unlike existing causality libraries, which mainly focus on effect estimation questions, with DoWhy-GCM, users can ask a wide range of additional causal questions, such as identifying the root causes of outliers and distributional changes, causal structure learning, attributing causal influences, and diagnosis of causal structures. To this end, DoWhy-GCM users first model cause-effect relations between variables in a system under study through a graphical causal model, fit the causal mechanisms of variables next, and then ask the causal question. All these steps take only a few lines of code in DoWhy-GCM. The library is available at https://github.com/py-why/dowhy.