# Identifying Causal Effects Under Functional Dependencies

arXiv: https://arxiv.org/abs/2403.04919 · HTML: https://mlsanity.com/paper/2403.04919/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 57 references that are in the map.
- First posted on arXiv 7 Mar 2024.

## Builds on (most cited first, 17 of 17)

- [A Differential Approach to Inference in Bayesian Networks](https://mlsanity.com/paper/1301.3847/) (2013)
- [Causal Networks: Semantics and Expressiveness](https://mlsanity.com/paper/1304.2379/) (2013)
- [Identifying Causal Effects via Context-specific Independence Relations](https://mlsanity.com/paper/2009.09768/) (2020)
- [On the Logic of Causal Models](https://mlsanity.com/paper/1304.2355/) (2013)
- [Separators and Adjustment Sets in Causal Graphs: Complete Criteria and an Algorithmic Framework](https://mlsanity.com/paper/1803.00116/) (2018)
- [Bucket Elimination: A Unifying Framework for Several Probabilistic Inference](https://mlsanity.com/paper/1302.3572/) (2013)
- [Counterfactuals and Policy Analysis in Structural Models](https://mlsanity.com/paper/1302.4929/) (2013)
- [Revisiting the General Identifiability Problem](https://mlsanity.com/paper/2206.01081/) (2022)
- [An Advance on Variable Elimination with Applications to Tensor-Based Computation](https://mlsanity.com/paper/2002.09320/) (2020)
- [Causal Expectation-Maximisation](https://mlsanity.com/paper/2011.02912/) (2020)
- [Approximating Counterfactual Bounds while Fusing Observational, Biased and Randomised Data Sources](https://mlsanity.com/paper/2307.16577/) (2023)
- [Enhancing Identification of Causal Effects by Pruning](https://mlsanity.com/paper/1806.07085/) (2018)
- [On the Complexity of Counterfactual Reasoning](https://mlsanity.com/paper/2211.13447/) (2022)
- [Simplifying Probabilistic Expressions in Causal Inference](https://mlsanity.com/paper/1806.07082/) (2018)
- [s-ID: Causal Effect Identification in a Sub-Population](https://mlsanity.com/paper/2309.02281/) (2023)
- [Tractable Bounding of Counterfactual Queries by Knowledge Compilation](https://mlsanity.com/paper/2310.03352/) (2023)
- [Approximations in Bayesian Belief Universe for Knowledge Based Systems](https://mlsanity.com/paper/1304.1101/) (2013)

## Built on by (most cited first, 3 of 3)

- [Constrained Identifiability of Causal Effects](https://mlsanity.com/paper/2412.02869/) (2024)
- [On the Granularity of Causal Effect Identifiability](https://mlsanity.com/paper/2510.16703/) (2025)
- [Interpretable Causal Discovery via Causal-Effect Constraints](https://mlsanity.com/paper/2608.12640/) (2026)

## Abstract (arXiv)

We study the identification of causal effects, motivated by two improvements to identifiability which can be attained if one knows that some variables in a causal graph are functionally determined by their parents (without needing to know the specific functions). First, an unidentifiable causal effect may become identifiable when certain variables are functional. Second, certain functional variables can be excluded from being observed without affecting the identifiability of a causal effect, which may significantly reduce the number of needed variables in observational data. Our results are largely based on an elimination procedure which removes functional variables from a causal graph while preserving key properties in the resulting causal graph, including the identifiability of causal effects.