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

03/03/2014

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by   Jonas Peters, et al.

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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.