# Causal Effect Identification from Multiple Incomplete Data Sources: A General Search-based Approach

arXiv: https://arxiv.org/abs/1902.01073 · HTML: https://mlsanity.com/paper/1902.01073/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Feb 2019.

## Built on by (most cited first, 16 of 16)

- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Revisiting the General Identifiability Problem](https://mlsanity.com/paper/2206.01081/) (2022)
- [Clustering and Structural Robustness in Causal Diagrams](https://mlsanity.com/paper/2111.04513/) (2021)
- [Efficient Online Estimation of Causal Effects by Deciding What to Observe](https://mlsanity.com/paper/2108.09265/) (2021)
- [On Identifiability of Conditional Causal Effects](https://mlsanity.com/paper/2306.11755/) (2023)
- [Experimental Design for Causal Effect Identification](https://mlsanity.com/paper/2205.02232/) (2022)
- [Estimating Joint Interventional Distributions from Marginal Interventional Data](https://mlsanity.com/paper/2409.01794/) (2024)
- [Clustering and Pruning in Causal Data Fusion](https://mlsanity.com/paper/2505.15215/) (2025)
- [Causal Effect Identification in a Sub-Population with Latent Variables](https://mlsanity.com/paper/2405.14547/) (2024)
- [Generalizing experimental findings: identification beyond adjustments](https://mlsanity.com/paper/2206.06699/) (2022)
- [Optimal Observation-Intervention Trade-Off in Optimisation Problems with Causal Structure](https://mlsanity.com/paper/2309.02287/) (2023)
- [Online Data Collection for Efficient Semiparametric Inference](https://mlsanity.com/paper/2411.03195/) (2024)
- [Optimal Policy Adaptation under Covariate Shift](https://mlsanity.com/paper/2501.08067/) (2025)
- [A Computational Theory for Efficient Mini Agent Evaluation with Causal Guarantees](https://mlsanity.com/paper/2503.21138/) (2025)
- [Causal identification with Y0](https://mlsanity.com/paper/2508.03167/) (2025)
- [Response to Discussions of "Causal and Counterfactual Views of Missing Data Models"](https://mlsanity.com/paper/2510.14694/) (2025)

## Abstract (arXiv)

Causal effect identification considers whether an interventional probability distribution can be uniquely determined without parametric assumptions from measured source distributions and structural knowledge on the generating system. While complete graphical criteria and procedures exist for many identification problems, there are still challenging but important extensions that have not been considered in the literature. To tackle these new settings, we present a search algorithm directly over the rules of do-calculus. Due to generality of do-calculus, the search is capable of taking more advanced data-generating mechanisms into account along with an arbitrary type of both observational and experimental source distributions. The search is enhanced via a heuristic and search space reduction techniques. The approach, called do-search, is provably sound, and it is complete with respect to identifiability problems that have been shown to be completely characterized by do-calculus. When extended with additional rules, the search is capable of handling missing data problems as well. With the versatile search, we are able to approach new problems such as combined transportability and selection bias, or multiple sources of selection bias. We perform a systematic analysis of bivariate missing data problems and study causal inference under case-control design. We also present the R package dosearch that provides an interface for a C++ implementation of the search.