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A graphical characterization of the largest chain graphs |
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| Authors: | Martin Volf,Milan Studený , |
| Affiliation: | aCzech Technical University Prague, Faculty of Nuclear Sciences and Physical Engineering, Department of Mathematics, Trojanova 13, Prague 12000, Czech Republic bInstitute of Information Theory and Automation, Academy of Sciences of Czech Republic, Pod vodárenskou věží 4, Prague 18208, Czech Republic cLaboratory of Intelligent Systems, University of Economics Prague, Ekonomická 957, Prague 14800, Czech Republic |
| Abstract: | The paper presents a graphical characterization of the largest chain graphs which serve as unique representatives of classes of Markov equivalent chain graphs. The characterization is a basis for an algorithm constructing, for a given chain graph, the largest chain graph equivalent to it. The algorithm was used to generate a catalog of the largest chain graphs with at most five vertices. Every item of the catalog contains the largest chain graph of a class of Markov equivalent chain graphs and an economical record of the induced independency model. |
| Keywords: | Graphical models Conditional independence Independency models Chain graphs Markov equivalence The largest chain graph Complex arrows Protected arrows |
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