M. Studeny: On non-graphical description of models of conditional independence structure. Paper presented at HSSS Workshop on Stochastic Systems for Individual Behaviours, January 22-23, 2001, Louvain la Neuve, Belgium.

Several graphical structural models, including some models with latent variables can be viewed as models of conditional independence structure. However, usual graphical methods do not allow one to describe all possible stochastic conditional independence structures. Therefore an attempt to develop a general method of mathematical description of conditional independence structures by means of certain integer-valued functions, called structural imsets, was made. The main part of the paper is an outline of this approach. The presented results concern the mathematical basis of this method. After exposition of theoretical background some open questions are discussed: the problem of internal computer representation of models, inferential problems and interpretation question. The paper is concluded by a cursory reflection on what are suitable learning strategies and relevant data generating procedures for models of conditional independence structure.

AMS classification 68T30

conditional independence structure
structural imset
marginally continuous measures

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