%0 Journal Article %1 Studeny2009 %A Studen�, Milan %A Vomlel, Jir� %D 2009 %J International Journal of Approximate Reasoning %K Bayesian network structure %N 2 %P 385 - 413 %R DOI: 10.1016/j.ijar.2008.09.001 %T A reconstruction algorithm for the essential graph %U http://www.sciencedirect.com/science/article/B6V07-4TK479C-1/2/5fcaf9e0b88e99264fbd18b5bde4f7c9 %V 50 %X 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.

@article{Studeny2009, 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.}, added-at = {2009-09-12T19:19:34.000+0200}, author = {Studen�, Milan and Vomlel, Jir�}, biburl = {https://www.bibsonomy.org/bibtex/29d80093fa0f32aace7ca956e67a518ac/mozaher}, doi = {DOI: 10.1016/j.ijar.2008.09.001}, file = {:Studeny2009.pdf:PDF}, interhash = {78c8ccabfc33fe63482ceee4f1eee5cc}, intrahash = {9d80093fa0f32aace7ca956e67a518ac}, issn = {0888-613X}, journal = {International Journal of Approximate Reasoning}, keywords = {Bayesian network structure}, note = {Special Section on The Imprecise Dirichlet Model and Special Section on Bayesian Robustness (Issues in Imprecise Probability)}, number = 2, owner = {Mozaherul Hoque}, pages = {385 - 413}, timestamp = {2009-09-12T19:19:43.000+0200}, title = {A reconstruction algorithm for the essential graph}, url = {http://www.sciencedirect.com/science/article/B6V07-4TK479C-1/2/5fcaf9e0b88e99264fbd18b5bde4f7c9}, volume = 50, year = 2009 }