# Causal Additive Models with Unobserved Causal Paths and Backdoor Paths

arXiv: https://arxiv.org/abs/2502.07646 · HTML: https://mlsanity.com/paper/2502.07646/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 55 references that are in the map.
- First posted on arXiv 11 Feb 2025.

## Builds on (most cited first, 16 of 16)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Causality for Machine Learning](https://mlsanity.com/paper/1911.10500/) (2019)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [Conditional independence testing based on a nearest-neighbor estimator of conditional mutual information](https://mlsanity.com/paper/1709.01447/) (2017)
- [Causal structure based root cause analysis of outliers](https://mlsanity.com/paper/1912.02724/) (2019)
- [Differentiable Causal Discovery Under Unmeasured Confounding](https://mlsanity.com/paper/2010.06978/) (2020)
- [Learning Linear Non-Gaussian Causal Models in the Presence of Latent Variables](https://mlsanity.com/paper/1908.03932/) (2019)
- [ParceLiNGAM: A causal ordering method robust against latent confounders](https://mlsanity.com/paper/1303.7410/) (2013)
- [Causal Discovery with Unobserved Confounding and non-Gaussian Data](https://mlsanity.com/paper/2007.11131/) (2020)
- [Causal Reasoning in the Presence of Latent Confounders via Neural ADMG Learning](https://mlsanity.com/paper/2303.12703/) (2023)
- [Identification of Causal Structure with Latent Variables Based on Higher Order Cumulants](https://mlsanity.com/paper/2312.11934/) (2023)
- [Causal Effect Identification in LiNGAM Models with Latent Confounders](https://mlsanity.com/paper/2406.02049/) (2024)
- [Assessing the overall and partial causal well-specification of nonlinear additive noise models](https://mlsanity.com/paper/2310.16502/) (2023)
- [Causal-discovery-based root-cause analysis and its application in time-series prediction error diagnosis](https://mlsanity.com/paper/2411.06990/) (2024)

## Built on by (most cited first, 5 of 5)

- [When Additive Noise Meets Unobserved Mediators: Bivariate Denoising Diffusion for Causal Discovery](https://mlsanity.com/paper/2506.23374/) (2025)
- [I-CAM-UV: Integrating Causal Graphs over Non-Identical Variable Sets Using Causal Additive Models with Unobserved Variables](https://mlsanity.com/paper/2603.03207/) (2026)
- [Beyond Additivity: Causal Discovery in Location-Scale Noise Models with Hidden Variables](https://mlsanity.com/paper/2606.08196/) (2026)
- [Operationalizing Longitudinal Causal Discovery Under Real-World Workflow Constraints](https://mlsanity.com/paper/2602.23800/) (2026)
- [Causal Discovery via Transformed Low-Rank Quantile Surfaces](https://mlsanity.com/paper/2609.16931/) (2026)

## Abstract (arXiv)

Causal additive models provide a tractable yet expressive framework for causal discovery in the presence of hidden variables. When unobserved backdoor or causal paths exist between two variables, their causal relationship is often unidentifiable under existing theories. We establish sufficient conditions under which causal directions can be identified in many such cases. These conditions rely on new characterizations of regression sets to determine independence among regression residuals and conditional independencies among observed variables. Building on these results, we introduce a search algorithm that incorporates these innovations and prove its soundness and completeness. Empirical evaluations demonstrate its competitive performance against state-of-the-art methods.