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Stratified exponential families: Graphical models and model selection
 ANNALS OF STATISTICS
, 2001
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Complexity Of Structural Models
, 1998
"... Complexity of a model of conditional independence structure is introduced as the least cardinality of a generating set. Four basic types of complexity are distinguished which depend on the type of generating. A method of calculation of complexity of a given conditional independence model is proposed ..."
Abstract

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Complexity of a model of conditional independence structure is introduced as the least cardinality of a generating set. Four basic types of complexity are distinguished which depend on the type of generating. A method of calculation of complexity of a given conditional independence model is proposed. The method is based on a more effective way of representation of the model by means of a list of dominant conditional independence statements. Prospects of the proposed approach are discussed in the end. AMS classification: 68T30, 62H05. Keywords: probabilistic model, semigraphoid, complexity, dominant triplet. 1 INTRODUCTION The most of structured models used in probabilistic reasoning and in multivariate statistics, especially graphical models, are models of probabilistic conditional independence structure. Verification of validity of such a stuctural model is based on statistical conditional independence tests. This leads to natural questions. Which conditional independence tests sh...