On Identifiability of Conditional Causal Effects

• URL: http://arxiv.org/abs/2306.11755v1
• Date: Mon, 19 Jun 2023 14:38:06 GMT
• Title: On Identifiability of Conditional Causal Effects
• Authors: Yaroslav Kivva, Jalal Etesami, Negar Kiyavash
• Abstract summary: We address the problem of identifiability of an arbitrary conditional causal effect given both the causal graph and a set of any observational and/or interventional distributions of the form $Q[S]:=P(S|do(Vsetminus S))$. We call this problem conditional generalized identifiability (c-gID in short) and prove the completeness of Pearl's $do$-calculus for the c-gID problem.
• Score: 24.95216517499459
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We address the problem of identifiability of an arbitrary conditional causal effect given both the causal graph and a set of any observational and/or interventional distributions of the form $Q[S]:=P(S|do(V\setminus S))$, where $V$ denotes the set of all observed variables and $S\subseteq V$. We call this problem conditional generalized identifiability (c-gID in short) and prove the completeness of Pearl's $do$-calculus for the c-gID problem by providing sound and complete algorithm for the c-gID problem. This work revisited the c-gID problem in Lee et al. [2020], Correa et al. [2021] by adding explicitly the positivity assumption which is crucial for identifiability. It extends the results of [Lee et al., 2019, Kivva et al., 2022] on general identifiability (gID) which studied the problem for unconditional causal effects and Shpitser and Pearl [2006b] on identifiability of conditional causal effects given merely the observational distribution $P(\mathbf{V})$ as our algorithm generalizes the algorithms proposed in [Kivva et al., 2022] and [Shpitser and Pearl, 2006b].

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