Causal Identification under Markov Equivalence
This work addresses a key challenge in causal inference for researchers who lack strong domain knowledge to specify unique causal graphs, offering a more robust method for effect estimation from observational data.
The paper tackles the problem of identifying causal effects when only a Markov equivalence class of causal graphs is known, rather than a unique graph, by developing an algorithm that computes effects from partial ancestral graphs (PAGs). The result is an algorithm that is strictly more powerful than the current state of the art, as demonstrated in the abstract.
Assessing the magnitude of cause-and-effect relations is one of the central challenges found throughout the empirical sciences. The problem of identification of causal effects is concerned with determining whether a causal effect can be computed from a combination of observational data and substantive knowledge about the domain under investigation, which is formally expressed in the form of a causal graph. In many practical settings, however, the knowledge available for the researcher is not strong enough so as to specify a unique causal graph. Another line of investigation attempts to use observational data to learn a qualitative description of the domain called a Markov equivalence class, which is the collection of causal graphs that share the same set of observed features. In this paper, we marry both approaches and study the problem of causal identification from an equivalence class, represented by a partial ancestral graph (PAG). We start by deriving a set of graphical properties of PAGs that are carried over to its induced subgraphs. We then develop an algorithm to compute the effect of an arbitrary set of variables on an arbitrary outcome set. We show that the algorithm is strictly more powerful than the current state of the art found in the literature.