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Biskup/Hartmann/2012b: Probabilistic Conditional Independence under Schema Certainty and Uncertainty

Bibtype Inproceedings
Bibkey Biskup/Hartmann/2012b
Author Biskup, Joachim and Hartmann, Sven and Link, Sebastian
Editor Eyke Hüllermeier and Sebastian Link and Thomas Fober and Bernhard Seeger
Title Probabilistic Conditional Independence under Schema Certainty and Uncertainty
Booktitle Scalable Uncertainty Management - 6th International Conference (SUM 2012)
Series LNCS
Volume 7520
Pages 365-378
Publisher Springer
Abstract Conditional independence provides an essential framework to
deal with knowledge and uncertainty in Artificial Intelligence, and is fundamental
in probability and multivariate statistics. Its associated implication
problem is paramount for building Bayesian networks. Saturated
conditional independencies form an important subclass of conditional independencies.
Under schema certainty, the implication problem of this
subclass is finitely axiomatizable and decidable in almost linear time. We
study the implication problem of saturated conditional independencies
under both schema certainty and uncertainty. Under schema certainty,
we establish a finite axiomatization with the following property: every
independency whose implication is dependent on the underlying schema
can be inferred by a single application of the so-called symmetry rule to
some independency whose implication is independent from the underlying
schema. Removing the symmetry rule from the axiomatization under
schema certainty results in an axiomatization for a notion of implication
that leaves the underlying schema undetermined. Hence, the symmetry
rule is just a means to infer saturated conditional independencies whose
implication is truly dependent on the schema.
Year 2012
Projekt SFB876-A5
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