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Causal Effect Identification in a Sub-Population with Latent Variables

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

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Extends sub-population causal effect identification (s-ID) to settings with latent variables by defining s-components and s-hedges, giving a sufficient graphical condition, a sound algorithm, and a reduction from s-Recoverability to s-ID.

Problem

Identifying a causal effect within a specific sub-population (P_X(Y | S=1)) from observational data of that sub-population when some variables are latent (s-ID with latent variables).

Approach

Generalizes c-components and hedges to s-components and s-hedges over an augmented ADMG with selection node S, yielding a graphical identifiability condition and recursive algorithm for s-ID under latent confounding, plus a reduction from s-Recoverability to s-ID.

Key results

• Gives a sufficient graphical condition (Theorem 1) for s-ID in ADMGs with latent variables, with s-Hedges as the obstruction.
• Proposes a sound recursive algorithm (sID / sID-Single) that returns an expression for P^S_X(Y) in terms of P(V|S=1) or Fail.
• Shows a reduction: s-Recoverability of P_X(Y) reduces to s-ID plus an m-separation condition (Theorem 3).

Surprising findings

• A causal effect identifiable in the ID setting (ignoring S) can be non-identifiable in the s-ID setting, illustrated by a constructed counterexample with two SCMs.

Limitations

• Soundness is proven but completeness of the algorithm is only conjectured.
• The appendix numerical experiment is the only empirical component; the work is primarily theoretical.

Experimental setup

Baselines: ID algorithm applied to sub-population data RC algorithm

Builds on: ID algorithm c-components hedge do-calculus s-ID (Abouei et al., 2023) s-Recoverability (RC algorithm)

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