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. 193-200.
In learning Bayesian networks one meets the problem of non-unique
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 integer-valued
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.
- essential graph
- standard imset
- reconstruction algorithm
scanned pdf copy (612kB) is available. Moreover,
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. Springer-Verlag, London, 2005.