2,656 research outputs found
Reasoning about Independence in Probabilistic Models of Relational Data
We extend the theory of d-separation to cases in which data instances are not
independent and identically distributed. We show that applying the rules of
d-separation directly to the structure of probabilistic models of relational
data inaccurately infers conditional independence. We introduce relational
d-separation, a theory for deriving conditional independence facts from
relational models. We provide a new representation, the abstract ground graph,
that enables a sound, complete, and computationally efficient method for
answering d-separation queries about relational models, and we present
empirical results that demonstrate effectiveness.Comment: 61 pages, substantial revisions to formalisms, theory, and related
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On the Intersection Property of Conditional Independence and its Application to Causal Discovery
This work investigates the intersection property of conditional independence.
It states that for random variables and we have that
independent of given and independent of given implies
independent of given . 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
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