# On the Intersection Property of Conditional Independence and its Application to Causal Discovery

arXiv: https://arxiv.org/abs/1403.0408 · HTML: https://mlsanity.com/paper/1403.0408/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Mar 2014.

## Built on by (most cited first, 6 of 6)

- [Uncovering Meanings of Embeddings via Partial Orthogonality](https://mlsanity.com/paper/2310.17611/) (2023)
- [Efficient Bayesian network structure learning via local Markov boundary search](https://mlsanity.com/paper/2110.06082/) (2021)
- [On Discovery of Local Independence over Continuous Variables via Neural Contextual Decomposition](https://mlsanity.com/paper/2405.07220/) (2024)
- [Conditions and Assumptions for Constraint-based Causal Structure Learning](https://mlsanity.com/paper/2103.13521/) (2021)
- [Assessing the overall and partial causal well-specification of nonlinear additive noise models](https://mlsanity.com/paper/2310.16502/) (2023)
- [Axiomatization of Interventional Probability Distributions](https://mlsanity.com/paper/2305.04479/) (2023)

## Abstract (arXiv)

This work investigates the intersection property of conditional independence. It states that for random variables A,B,C and X we have that X independent of A given B,C and X independent of B given A,C implies X independent of (A,B) given C. Under the assumption that the joint distribution has a continuous density, we provide necessary and sufficient conditions under which the intersection property holds. The result has direct applications to causal inference: it leads to strictly weaker conditions under which the graphical structure becomes identifiable from the joint distribution of an additive noise model.