M. Studeny, J. Vomlel:
A reconstruction algorithm for the essential graph.
International Journal of Approximate Reasoning 50 (2009),
n. 2, pp. 385413.
 Abstract

A standard graphical representative of a Bayesian network structure
is a special chain graph, known as an essential graph.
An alternative algebraic approach to the mathematical description of
this statistical model uses instead a certain integervalued vector,
known as a standard imset. We give a direct formula for the
translation of any chain graph describing a Bayesian network
structure into the standard imset. Moreover, we present a twostage
algorithm which makes it possible to reconstruct the essential graph
on the basis of the standard imset. The core of this paper is the
proof of the correctness of the algorithm.
 AMS classification 68T30, 05C90
 Keywords
 Bayesian network structure
 chain graph
 essential graph
 standard imset

A
pdf version of the published paper (708kB) is already openaccess available.
The paper is (quite a lot) extended version of the conference paper:
The paper builds on the results from these previous publications:
 M. Studeny:
Probabilistic Conditional Independence Structures. SpringerVerlag, London, 2005.
 S.A. Andersson, D. Madigan, M.D. Perlman:
A characterization of Markov equivalence classes for acyclic
digraphs. Annals of Statistics 25 (1997), pp. 505541.
Moreover, it uses some of the results of a parallel paper: