Identification of Conditional Causal Effects under Markov Equivalence

Causal identification is the problem of deciding whether a post-interventional distribution is computable from a combination of qualitative knowledge about the data-generating process, which is encoded in a causal diagram, and an observational distribution. A generalization of this problem restricts the qualitative knowledge to a class of Markov equivalent causal diagrams, which, unlike a single, fully-specified causal diagram, can be inferred from the observational distribution. Recent work by (Jaber et al., 2019a) devised a complete algorithm for the identification of unconditional causal effects given a Markov equivalence class of causal diagrams. However, there are identifiable conditional causal effects that cannot be handled by that algorithm. In this work, we derive an algorithm to identify conditional effects, which are particularly useful for evaluating conditional plans or policies.