linear inequalities; polyhedral sets; Bayesian networks; information; entropy
We investigate solution sets of a special kind of linear inequality systems. In particular, we derive characterizations of these sets in terms of minimal solution sets. The studied inequalities emerge as information inequalities in the context of Bayesian networks. This allows to deduce structural properties of Bayesian networks, which is important within causal inference.
 Martini, H., Wenzel, W.: Illumination and visibility problems in terms of closure operators
. Beiträge zur Algebra und Geometrie 45 (2004), 2, 607-614. MR 2093030
| Zbl 1074.52001
 Steudel, B., Ay, N.: Information-theoretic inference of common ancestors. Submitted. ArXiv preprint (2010) arXiv:1010.5720.