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s-ID: Causal Effect Identification in a Sub-population

AAAI 2024 · Probabilistic and scientific modeling › Causal discovery · approach: Causal effect identification · 0 citations (OpenAlex)

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Introduces s-ID, identifying interventional effects in a sub-population from only sub-population observational data, gives necessary and sufficient graphical conditions and a sound and complete algorithm.

Problem

Causal effect identification when the only available observational data comes from a target sub-population (selection via an auxiliary variable S), rather than the whole population, which existing ID, c-ID, gID, and S-recoverability settings cannot handle.

Approach

Model the sub-population with an auxiliary child variable S of the causal graph and show that the sub-population causal effect P_X(Y|S=1) is identifiable from P(V|S=1) iff X is not an ancestor of S or X d-separates from Y given S in the graph with X's incoming edges removed; provides a sound and complete algorithm.

Key results

• Necessary and sufficient graphical condition for s-ID in the singleton case: X not in Anc(S) or X independent of Y given S in the graph with X's incoming edges removed.
• Multivariate case extends the condition to X1 = X ∩ Anc(S) with a d-separation check, yielding a sound and complete algorithm running in O(n+m) time.
• Shows via examples that ignoring the sub-population and applying standard ID can yield erroneous inference.

Surprising findings

• In a sub-population, the causal effect can be non-trivial even when X has no causal effect on Y in the population, due to selection-induced dependence between X and Y in P(V|S=1).

Limitations

• Assumes all variables in the sub-population are observable; no latent variables.
• Addresses only identification, not estimation or sensitivity analysis.

Experimental setup

Baselines: ID algorithm c-ID c-gID S-recoverability

Builds on: do-calculus ID problem (Shpitser and Pearl) c-ID S-recoverability gID

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