Characteristic Properties of Equivalent Structures in Compositional Models

0359927 - ÚTIA 2012 RIV US eng J - Journal Article
Kratochvíl, Václav
Characteristic Properties of Equivalent Structures in Compositional Models.
International Journal of Approximate Reasoning. Roč. 52, č. 5 (2011), s. 599-612. ISSN 0888-613X. E-ISSN 1873-4731
R&D Projects: GA MŠMT 1M0572; GA ČR GA201/09/1891; GA ČR GEICC/08/E010
Grant - others:GA MŠk(CZ) 2C06019
Institutional research plan: CEZ:AV0Z10750506
Keywords : Equivalence problem * Compositional model * Persegram * Characteristic properties
Subject RIV: BA - General Mathematics
Impact factor: 1.948, year: 2011
http://library.utia.cas.cz/separaty/2011/MTR/kratochvil-0359927.pdf

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.
Permanent Link: http://hdl.handle.net/11104/0197607