Identifying Causal Effects via Context-specific Independence Relations
This work addresses a fundamental limitation in causal inference for researchers and practitioners, providing a novel method to handle CSI-relations, though it is incremental as it builds upon existing do-calculus.
The paper tackles the problem of causal effect identification when context-specific independence (CSI) relations exist, showing that deciding non-identifiability is NP-hard and proposing a sound calculus and automated procedure that extends standard do-calculus to obtain previously unobtainable identifying formulas, with examples showing that a few CSI-relations can turn non-identifiable instances into identifiable ones.
Causal effect identification considers whether an interventional probability distribution can be uniquely determined from a passively observed distribution in a given causal structure. If the generating system induces context-specific independence (CSI) relations, the existing identification procedures and criteria based on do-calculus are inherently incomplete. We show that deciding causal effect non-identifiability is NP-hard in the presence of CSIs. Motivated by this, we design a calculus and an automated search procedure for identifying causal effects in the presence of CSIs. The approach is provably sound and it includes standard do-calculus as a special case. With the approach we can obtain identifying formulas that were unobtainable previously, and demonstrate that a small number of CSI-relations may be sufficient to turn a previously non-identifiable instance to identifiable.