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.

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