# On Identifiability of Conditional Causal Effects

arXiv: https://arxiv.org/abs/2306.11755 · HTML: https://mlsanity.com/paper/2306.11755/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 19 references that are in the map.
- First posted on arXiv 19 Jun 2023.

## Builds on (most cited first, 4 of 4)

- [Nested Counterfactual Identification from Arbitrary Surrogate Experiments](https://mlsanity.com/paper/2107.03190/) (2021)
- [Causal Effect Identification from Multiple Incomplete Data Sources: A General Search-based Approach](https://mlsanity.com/paper/1902.01073/) (2019)
- [Revisiting the General Identifiability Problem](https://mlsanity.com/paper/2206.01081/) (2022)
- [Causal Effect Identification with Context-specific Independence Relations of Control Variables](https://mlsanity.com/paper/2110.12064/) (2021)

## Built on by (most cited first, 4 of 4)

- [Parameter identification in linear non-Gaussian causal models under general confounding](https://mlsanity.com/paper/2405.20856/) (2024)
- [s-ID: Causal Effect Identification in a Sub-Population](https://mlsanity.com/paper/2309.02281/) (2023)
- [Causal Effect Identification in a Sub-Population with Latent Variables](https://mlsanity.com/paper/2405.14547/) (2024)
- [CIDER-FM: Foundation Models for Causal Inference from Diverse Experimental Regimes](https://mlsanity.com/paper/2609.39523/) (2026)

## Abstract (arXiv)

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)), where V denotes the set of all observed variables and Ssubseteq 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(V) as our algorithm generalizes the algorithms proposed in [Kivva et al., 2022] and [Shpitser and Pearl, 2006b].