Jornal article

International Journal of Approximate Reasoning

2011

5 (2011)

599-612

0888-613X

Ing. Václav Kratochvíl (ÚTIA - Oddělení matematické teorie rozhodování)

Equivalence problem, Compositional model, Persegram, Charact

Compositional model theory serves as an alternative to Bayesian networks. Every compositional model over a finite non-empty set of variables N is uniquely defined by its generating sequence – an ordered set of low-dimensional probability distributions. A generating sequence structure induces a system of conditional independence statements over N valid for every multidimensional distribution represented by a compositional model with this structure. The equivalence problem is how to characterise whether all independence statements induced by structure P are induced by a second structure P and vice versa. This problem can be solved in several ways. A partial solution of the so-called direct characterisation of an equivalence problem is represented here. We deduce and describe three properties of equivalent structures necessary for equivalence of the respective structures. We call them characteristic properties of classes of equivalent structures.