# Revisiting the General Identifiability Problem

arXiv: https://arxiv.org/abs/2206.01081 · HTML: https://mlsanity.com/paper/2206.01081/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 13 references that are in the map.
- First posted on arXiv 2 Jun 2022.

## Builds on (most cited first, 2 of 2)

- [Causal Effect Identification from Multiple Incomplete Data Sources: A General Search-based Approach](https://mlsanity.com/paper/1902.01073/) (2019)
- [Causal Effect Identification with Context-specific Independence Relations of Control Variables](https://mlsanity.com/paper/2110.12064/) (2021)

## Built on by (most cited first, 13 of 13)

- [Parameter identification in linear non-Gaussian causal models under general confounding](https://mlsanity.com/paper/2405.20856/) (2024)
- [On Identifiability of Conditional Causal Effects](https://mlsanity.com/paper/2306.11755/) (2023)
- [Causal Effect Identification in Uncertain Causal Networks](https://mlsanity.com/paper/2208.04627/) (2022)
- [s-ID: Causal Effect Identification in a Sub-Population](https://mlsanity.com/paper/2309.02281/) (2023)
- [Identifying Causal Effects Under Functional Dependencies](https://mlsanity.com/paper/2403.04919/) (2024)
- [Fast Proxy Experiment Design for Causal Effect Identification](https://mlsanity.com/paper/2407.05330/) (2024)
- [Characterization and Learning of Causal Graphs from Hard Interventions](https://mlsanity.com/paper/2505.01037/) (2025)
- [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)
- [On Transportability for Structural Causal Bandits](https://mlsanity.com/paper/2511.17953/) (2025)
- [Notes on Forr'e's Notion of Conditional Independence and Causal Calculus for Continuous Variables](https://mlsanity.com/paper/2603.24333/) (2026)
- [Online Data Collection for Efficient Semiparametric Inference](https://mlsanity.com/paper/2411.03195/) (2024)
- [Optimal Experiments for Partial Causal Effect Identification](https://mlsanity.com/paper/2605.06993/) (2026)

## Abstract (arXiv)

We revisit the problem of general identifiability originally introduced in [Lee et al., 2019] for causal inference and note that it is necessary to add positivity assumption of observational distribution to the original definition of the problem. We show that without such an assumption the rules of do-calculus and consequently the proposed algorithm in [Lee et al., 2019] are not sound. Moreover, adding the assumption will cause the completeness proof in [Lee et al., 2019] to fail. Under positivity assumption, we present a new algorithm that is provably both sound and complete. A nice property of this new algorithm is that it establishes a connection between general identifiability and classical identifiability by Pearl [1995] through decomposing the general identifiability problem into a series of classical identifiability sub-problems.