On the Intersection Property of Conditional Independence and its Application to Causal Discovery
- Journal Article
Rechte / LizenzIn Copyright - Non-Commercial Use Permitted
This work investigates the intersection property of conditional independence. It states that for random variables A,B,C and X we have that X⊥⊥A|B,C and X⊥⊥B|A,C implies X⊥⊥(A,B)|C. Here, “ ⊥⊥” stands for statistical independence. Under the assumption that the joint distribution has a density that is continuous in A,B and C, 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. Mehr anzeigen
Zeitschrift / SerieJournal of Causal Inference
Seiten / Artikelnummer
ThemaProbability theory; Causal discovery; Graphical models
Organisationseinheit03502 - Bühlmann, Peter L. / Bühlmann, Peter L.
AnmerkungenIt was possible to publish this article open access thanks to a Swiss National Licence with the publisher.