Properties of semi-elementary imsets as sums of elementary imsets
Statistics Theory
2011-08-22 v1 Statistics Theory
Abstract
We study properties of semi-elementary imsets and elementary imsets introduced by Studeny (2005). The rules of the semi-graphoid axiom (decomposition, weak union and contraction) for conditional independence statements can be translated into a simple identity among three semi-elementary imsets. By recursively applying the identity, any semi-elementary imset can be written as a sum of elementary imsets, which we call a representation of the semi-elementary imset. A semi-elementary imset has many representations. We study properties of the set of possible representations of a semi-elementary imset and prove that all representations are connected by relations among four elementary imsets.
Keywords
Cite
@article{arxiv.1105.6027,
title = {Properties of semi-elementary imsets as sums of elementary imsets},
author = {Takuya Kashimura and Tomonari Sei and Akimichi Takemura and Kentaro Tanaka},
journal= {arXiv preprint arXiv:1105.6027},
year = {2011}
}