M. Studeny, J. Vomlel:
Transition between graphical and algebraic representatives of Bayesian network models.
In Proceedings of the 2nd European Workshop on Probabilistic Graphical Models
(P. Lucas ed.), University of Nijmegen 2004, pp. 193200.
 Abstract

In learning Bayesian networks one meets the problem of nonunique
graphical description of the respective statistical model. One way to
avoid this problem is to use special chain graphs, named essential
graphs. An alternative algebraic approach uses certain integervalued
vectors, named standard imsets, instead. In this
paper we present algorithms which make it possible to transform
graphical representatives into algebraic ones and conversely.
A direct formula is a basis for translation of any chain graph
equivalent to a Bayesian network into a standard imset. An inverse
algorithm, which gives the essential graph, has two stages.
The middle result of this procedure is a certain sequence of sets
of variables, which can be turned into a hierarchical junction
tree. We present both the mathematical theory and the algorithms,
which we implemented in the R language.
 Keywords
 essential graph
 standard imset
 reconstruction algorithm
 A
scanned pdf copy (612kB) is available. Moreover,
A
pdf copy of an extended version (a converted postscript) (198kB) is available.
The paper builds partially on Chapter 8 from
 M. Studeny:
Probabilistic Conditional Independence Structures. SpringerVerlag, London, 2005.