Characteristic properties of equivalent structures in compositional models |
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Authors: | Václav Kratochvíl |
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Institution: | Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod Vodárenskou vě?í 4, 182 08 Praha 8, Czech Republic |
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Abstract: | Compositional model theory serves as an alternative approach to multidimensional probability distribution representation and processing. 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. |
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Keywords: | Equivalence problem Compositional model Persegram Characteristic properties |
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