# Causal Effect Identification with Context-specific Independence Relations of Control Variables

arXiv: https://arxiv.org/abs/2110.12064 · HTML: https://mlsanity.com/paper/2110.12064/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 30 references that are in the map.
- First posted on arXiv 22 Oct 2021.

## Builds on (most cited first, 9 of 9)

- [Context-Specific Independence in Bayesian Networks](https://mlsanity.com/paper/1302.3562/) (2013)
- [Probabilistic Evaluation of Sequential Plans from Causal Models with Hidden Variables](https://mlsanity.com/paper/1302.4977/) (2013)
- [Identifying Causal Effects via Context-specific Independence Relations](https://mlsanity.com/paper/2009.09768/) (2020)
- [A Recursive Markov Boundary-Based Approach to Causal Structure Learning](https://mlsanity.com/paper/2010.04992/) (2020)
- [A Bayesian Approach to Learning Bayesian Networks with Local Structure](https://mlsanity.com/paper/1302.1528/) (2013)
- [Labeled Directed Acyclic Graphs: a generalization of context-specific independence in directed graphical models](https://mlsanity.com/paper/1310.1187/) (2013)
- [An Interventionist Approach to Mediation Analysis](https://mlsanity.com/paper/2008.06019/) (2020)
- [Testing Identifiability of Causal Effects](https://mlsanity.com/paper/1302.4948/) (2013)
- [Stratified Graphical Models - Context-Specific Independence in Graphical Models](https://mlsanity.com/paper/1309.6415/) (2013)

## Built on by (most cited first, 8 of 8)

- [Revisiting the General Identifiability Problem](https://mlsanity.com/paper/2206.01081/) (2022)
- [Causal Imitability Under Context-Specific Independence Relations](https://mlsanity.com/paper/2306.00585/) (2023)
- [On Identifiability of Conditional Causal Effects](https://mlsanity.com/paper/2306.11755/) (2023)
- [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)
- [Staged Event Trees for Transparent Treatment Effect Estimation](https://mlsanity.com/paper/2509.26265/) (2025)
- [On the Granularity of Causal Effect Identifiability](https://mlsanity.com/paper/2510.16703/) (2025)
- [Partially Observed Structural Causal Models](https://mlsanity.com/paper/2605.03268/) (2026)

## Abstract (arXiv)

We study the problem of causal effect identification from observational distribution given the causal graph and some context-specific independence (CSI) relations. It was recently shown that this problem is NP-hard, and while a sound algorithm to learn the causal effects is proposed in Tikka et al. (2019), no complete algorithm for the task exists. In this work, we propose a sound and complete algorithm for the setting when the CSI relations are limited to observed nodes with no parents in the causal graph. One limitation of the state of the art in terms of its applicability is that the CSI relations among all variables, even unobserved ones, must be given (as opposed to learned). Instead, We introduce a set of graphical constraints under which the CSI relations can be learned from mere observational distribution. This expands the set of identifiable causal effects beyond the state of the art.