# Latent Variable Causal Discovery under Selection Bias

arXiv: https://arxiv.org/abs/2512.11219 · HTML: https://mlsanity.com/paper/2512.11219/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 59 references that are in the map.
- First posted on arXiv 12 Dec 2025.

## Builds on (most cited first, 15 of 15)

- [Learning latent causal graphs via mixture oracles](https://mlsanity.com/paper/2106.15563/) (2021)
- [Latent Hierarchical Causal Structure Discovery with Rank Constraints](https://mlsanity.com/paper/2210.01798/) (2022)
- [Nested Markov Properties for Acyclic Directed Mixed Graphs](https://mlsanity.com/paper/1701.06686/) (2017)
- [Fast Scalable and Accurate Discovery of DAGs Using the Best Order Score Search and Grow-Shrink Trees](https://mlsanity.com/paper/2310.17679/) (2023)
- [A Versatile Causal Discovery Framework to Allow Causally-Related Hidden Variables](https://mlsanity.com/paper/2312.11001/) (2023)
- [Local Constraint-Based Causal Discovery under Selection Bias](https://mlsanity.com/paper/2203.01848/) (2022)
- [Independence Testing-Based Approach to Causal Discovery under Measurement Error and Linear Non-Gaussian Models](https://mlsanity.com/paper/2210.11021/) (2022)
- [Gene Regulatory Network Inference in the Presence of Dropouts: a Causal View](https://mlsanity.com/paper/2403.15500/) (2024)
- [When Selection Meets Intervention: Additional Complexities in Causal Discovery](https://mlsanity.com/paper/2503.07302/) (2025)
- [Detecting and Identifying Selection Structure in Sequential Data](https://mlsanity.com/paper/2407.00529/) (2024)
- [On Testability of the Front-Door Model via Verma Constraints](https://mlsanity.com/paper/2203.00161/) (2022)
- [Identification of Causal Structure with Latent Variables Based on Higher Order Cumulants](https://mlsanity.com/paper/2312.11934/) (2023)
- [Local Causal Discovery with Linear non-Gaussian Cyclic Models](https://mlsanity.com/paper/2403.14843/) (2024)
- [On the Parameter Identifiability of Partially Observed Linear Causal Models](https://mlsanity.com/paper/2407.16975/) (2024)
- [Identifying Selections for Unsupervised Subtask Discovery](https://mlsanity.com/paper/2410.21616/) (2024)

## Built on by (most cited first, 7 of 7)

- [Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learning](https://mlsanity.com/paper/2603.04780/) (2026)
- [Consistency evaluation of benchmarks used for causal discovery](https://mlsanity.com/paper/2606.01789/) (2026)
- [Towards a holistic understanding of Selection Bias for Causal Effect Identification](https://mlsanity.com/paper/2605.13430/) (2026)
- [Causal Modeling of Selection in Evolution](https://mlsanity.com/paper/2606.05689/) (2026)
- [Discrete Causal Representations from Heterogeneous Domains: A Bayesian Approach with Social Survey Applications](https://mlsanity.com/paper/2606.06288/) (2026)
- [Identifying Structural Biases from Causal Mechanism Shifts](https://mlsanity.com/paper/2606.18834/) (2026)
- [Causal Discovery Under Hard Selection Bias: A New Robust Score-Matching Approach](https://mlsanity.com/paper/2610.18075/) (2026)

## Abstract (arXiv)

Addressing selection bias in latent variable causal discovery is important yet underexplored, largely due to a lack of suitable statistical tools: While various tools beyond basic conditional independencies have been developed to handle latent variables, none have been adapted for selection bias. We make an attempt by studying rank constraints, which, as a generalization to conditional independence constraints, exploits the ranks of covariance submatrices in linear Gaussian models. We show that although selection can significantly complicate the joint distribution, interestingly, the ranks in the biased covariance matrices still preserve meaningful information about both causal structures and selection mechanisms. We provide a graph-theoretic characterization of such rank constraints. Using this tool, we demonstrate that the one-factor model, a classical latent variable model, can be identified under selection bias. Simulations and real-world experiments confirm the effectiveness of using our rank constraints.