%0 Journal Article
%T On the Intersection Property of Conditional Independence and its Application to Causal Discovery
%A Jonas Peters
%J Statistics
%D 2014
%I arXiv
%X 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.
%U http://arxiv.org/abs/1403.0408v2