Stable Independance and Complexity of Representation
This work addresses a theoretical problem in AI/ML for researchers dealing with independence relations, but it appears incremental as it builds upon prior dominance-based representations.
The paper tackles the problem of representing independence relations more compactly by introducing the concept of stability, which reduces the complexity of many relations compared to existing methods.
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.