TY - GEN

T1 - Characteristic imset

T2 - 5th European Workshop on Probabilistic Graphical Models, PGM 2010

AU - Studený, Milan

AU - Hemmecke, Raymond

AU - Lindner, Silvia

PY - 2010

Y1 - 2010

N2 - First, we recall the basic idea of an algebraic and geometric approach to learning a Bayesian network (BN) structure proposed in (Studený, Vomlel and Hemmecke, 2010): to represent every BN structure by a certain uniquely determined vector. The original proposal was to use a so-called standard imset which is a vector having integers as components, as an algebraic representative of a BN structure. In this paper we propose an even simpler algebraic representative called the characteristic imset. It is 0-1-vector obtained from the standard imset by an affine transformation. This implies that every reasonable quality criterion is an affine function of the characteristic imset. The characteristic imset is much closer to the graphical description: we establish a simple relation to any chain graph without flags that defines the BN structure. In particular, we are interested in the relation to the essential graph, which is a classic graphical BN structure representative. In the end, we discuss two special cases in which the use of characteristic imsets particularly simplifies things: learning decomposable models and (undirected) forests.

AB - First, we recall the basic idea of an algebraic and geometric approach to learning a Bayesian network (BN) structure proposed in (Studený, Vomlel and Hemmecke, 2010): to represent every BN structure by a certain uniquely determined vector. The original proposal was to use a so-called standard imset which is a vector having integers as components, as an algebraic representative of a BN structure. In this paper we propose an even simpler algebraic representative called the characteristic imset. It is 0-1-vector obtained from the standard imset by an affine transformation. This implies that every reasonable quality criterion is an affine function of the characteristic imset. The characteristic imset is much closer to the graphical description: we establish a simple relation to any chain graph without flags that defines the BN structure. In particular, we are interested in the relation to the essential graph, which is a classic graphical BN structure representative. In the end, we discuss two special cases in which the use of characteristic imsets particularly simplifies things: learning decomposable models and (undirected) forests.

UR - http://www.scopus.com/inward/record.url?scp=79954420130&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:79954420130

SN - 9789526033143

T3 - Proceedings of the 5th European Workshop on Probabilistic Graphical Models, PGM 2010

SP - 257

EP - 264

BT - Proceedings of the 5th European Workshop on Probabilistic Graphical Models, PGM 2010

Y2 - 13 September 2010 through 15 September 2010

ER -