# Local Constraint-Based Causal Discovery under Selection Bias

arXiv: https://arxiv.org/abs/2203.01848 · HTML: https://mlsanity.com/paper/2203.01848/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 38 references that are in the map.
- First posted on arXiv 3 Mar 2022.

## Builds on (most cited first, 8 of 8)

- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [Foundations of Structural Causal Models with Cycles and Latent Variables](https://mlsanity.com/paper/1611.06221/) (2016)
- [Learning Sparse Causal Models is not NP-hard](https://mlsanity.com/paper/1309.6824/) (2013)
- [Causal Discovery in the Presence of Missing Data](https://mlsanity.com/paper/1807.04010/) (2018)
- [Markov Properties for Graphical Models with Cycles and Latent Variables](https://mlsanity.com/paper/1710.08775/) (2017)
- [Constraint-Based Causal Discovery using Partial Ancestral Graphs in the presence of Cycles](https://mlsanity.com/paper/2005.00610/) (2020)
- [Boosting Local Causal Discovery in High-Dimensional Expression Data](https://mlsanity.com/paper/1910.02505/) (2019)

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

- [Discovering Causal Relations and Equations from Data](https://mlsanity.com/paper/2305.13341/) (2023)
- [Local Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/2405.16225/) (2024)
- [Local Causal Discovery for Estimating Causal Effects](https://mlsanity.com/paper/2302.08070/) (2023)
- [When Selection Meets Intervention: Additional Complexities in Causal Discovery](https://mlsanity.com/paper/2503.07302/) (2025)
- [Towards Practical Federated Causal Structure Learning](https://mlsanity.com/paper/2306.09433/) (2023)
- [Detecting and Identifying Selection Structure in Sequential Data](https://mlsanity.com/paper/2407.00529/) (2024)
- [Gene Regulatory Network Inference in the Presence of Selection Bias and Latent Confounders](https://mlsanity.com/paper/2501.10124/) (2025)
- [Latent Variable Causal Discovery under Selection Bias](https://mlsanity.com/paper/2512.11219/) (2025)
- [Identifying Selections for Unsupervised Subtask Discovery](https://mlsanity.com/paper/2410.21616/) (2024)
- [Amortized Conditional Independence Testing](https://mlsanity.com/paper/2502.20925/) (2025)
- [Can LLMs Assist Expert Elicitation for Probabilistic Causal Modeling?](https://mlsanity.com/paper/2504.10397/) (2025)
- [From Local to Cluster: A Unified Framework for Causal Discovery with Latent Variables](https://mlsanity.com/paper/2604.22416/) (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)
- [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)

We consider the problem of discovering causal relations from independence constraints selection bias in addition to confounding is present. While the seminal FCI algorithm is sound and complete in this setup, no criterion for the causal interpretation of its output under selection bias is presently known. We focus instead on local patterns of independence relations, where we find no sound method for only three variable that can include background knowledge. Y-Structure patterns are shown to be sound in predicting causal relations from data under selection bias, where cycles may be present. We introduce a finite-sample scoring rule for Y-Structures that is shown to successfully predict causal relations in simulation experiments that include selection mechanisms. On real-world microarray data, we show that a Y-Structure variant performs well across different datasets, potentially circumventing spurious correlations due to selection bias.