M. Studeny, J. Vomlel: A reconstruction algorithm for the essential graph. International Journal of Approximate Reasoning 50 (2009), n. 2, pp. 385-413.

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

Bayesian network structure
chain graph
essential graph
standard imset

A pdf version of the published paper (708kB) is already open-access available.

The paper is (quite a lot) extended version of the conference paper:

The paper builds on the results from these previous publications:

Moreover, it uses some of the results of a parallel paper: