Stable Independance and Complexity of Representation

TL;DR

This paper introduces a stability-based approach to representing independence relations more compactly, reducing complexity and improving understanding of the structure of these relations.

Contribution

It proposes a new stability concept for independence representation, along with an algorithm, demonstrating lower complexity in many cases compared to existing methods.

Findings

Many independence relations have lower complexity with the new stability approach.

The proposed algorithm effectively constructs stable, compact representations.

Stability enhances the understanding of independence relation structures.

Abstract

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.