M. Studeny, J. Vomlel:
A reconstruction algorithm for the essential graph.
International Journal of Approximate Reasoning 50 (2009),
pp. 385-413.
- 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 integer-valued 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 two-stage
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
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A
pdf version of the preprint (464kB) is available.
The paper is (quite a lot) extended version of the conference paper:
- 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.
The paper builds on the results from these previous publications:
- M. Studeny:
Probabilistic Conditional Independence Structures. Springer-Verlag, 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. 505-541.
- M. Studeny, A. Roverato, S. Stepanova:
Two operations of merging and splitting components in a chain graph.
Kybernetika 45 (2009), n. 2, pp. 208-248.
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A
pdf version of the published paper (451kB) is available.