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Stable Independance and Complexity of Representation
Jul 11, 2012
The representation of independence relations generally builds upon the well-known semigraphoid axioms of independence. Recently, a representation has been proposed that captures a set of dominant statements of an independence relation from which any other statement can be generated by means of the axioms; the cardinality of this set is taken to indicate the complexity of the relation. Building upon the idea of dominance, we introduce the concept of stability to provide for a more compact representation of independence. We give an associated algorithm for establishing such a representation.We show that, with our concept of stability, many independence relations are found to be of lower complexity than with existing representations.
Stable Independence in Perfect Maps
Jul 04, 2012
With the aid of the concept of stable independence we can construct, in an efficient way, a compact representation of a semi-graphoid independence relation. We show that this representation provides a new necessary condition for the existence of a directed perfect map for the relation. The test for this condition is based to a large extent on the transitivity property of a special form of d-separation. The complexity of the test is linear in the size of the representation. The test, moreover, brings the additional benefit that it can be used to guide the early stages of network construction.