# Bayesian network structure learning with causal effects in the presence of latent variables

arXiv: https://arxiv.org/abs/2005.14381 · HTML: https://mlsanity.com/paper/2005.14381/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2020.

## Built on by (most cited first, 8 of 8)

- [A survey of Bayesian Network structure learning](https://mlsanity.com/paper/2109.11415/) (2021)
- [Causal Structure Learning: a Combinatorial Perspective](https://mlsanity.com/paper/2206.01152/) (2022)
- [Recursive Causal Structure Learning in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/2110.12036/) (2021)
- [Integer Programming for Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/2102.03129/) (2021)
- [Open problems in causal structure learning: A case study of COVID-19 in the UK](https://mlsanity.com/paper/2305.03859/) (2023)
- [Hybrid Bayesian network discovery with latent variables by scoring multiple interventions](https://mlsanity.com/paper/2112.10574/) (2021)
- [Covariate Dependent Mixture of Bayesian Networks](https://mlsanity.com/paper/2501.05745/) (2025)
- [Uncovering Bias Mechanisms in Observational Studies](https://mlsanity.com/paper/2506.01191/) (2025)

## Abstract (arXiv)

Latent variables may lead to spurious relationships that can be misinterpreted as causal relationships. In Bayesian Networks (BNs), this challenge is known as learning under causal insufficiency. Structure learning algorithms that assume causal insufficiency tend to reconstruct the ancestral graph of a BN, where bi-directed edges represent confounding and directed edges represent direct or ancestral relationships. This paper describes a hybrid structure learning algorithm, called CCHM, which combines the constraint-based part of cFCI with hill-climbing score-based learning. The score-based process incorporates Pearl s do-calculus to measure causal effects and orientate edges that would otherwise remain undirected, under the assumption the BN is a linear Structure Equation Model where data follow a multivariate Gaussian distribution. Experiments based on both randomised and well-known networks show that CCHM improves the state-of-the-art in terms of reconstructing the true ancestral graph.