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MAINTAINING OF INTERNAL CONSISTENCY OF ALGEBRAIC BAYESIAN NETWORKS WITH LINEAR AND STELLATE STRUCTURE

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Subject of Research. When working with algebraic Bayesian networks, it is necessary to ensure their correctness in terms of the consistency of the probability estimates of their constituent elements.There are several approaches to automating the maintenance of consistency, characterized by their computational complexity (execution time). This complexity depends on the network structure and the chosen type of consistency. The time for internal consistency maintenance  in algebraic Bayesian networks with linear and stellate structure is compared with the time for consistency maintenance of a knowledge pattern covering such networks. The comparison is based on statistical estimates. Method.The essence of the method lies in reducing the number of variables and conditions in linear programming problems which solution ensures the maintenance of internal consistency. An experiment was carried out demonstrating the differences between the time of consistency maintenance for different algebraic Bayesian networks with a global structure. Main Results. An improved version of the algorithm for internal consistency maintenance is presented.Solvable linear programming problems are simplified in comparison with the previous version of the algorithm. Two theorems are formulated and proved, refining the estimates of the number of variables and conditions in the linear programming problems to be solved, as well as the number of the problems themselves. An experiment is performed, which showed that the proposed software implementation of internal consistency maintenanceis superior in working time to software implementation of the consistency maintenanceof a complete knowledge pattern. Practical Relevance. The results obtained can be applied in machine learning of algebraic Bayesian networks (including the synthesis of their global structures). The proposed method provides optimal synthesis of global network structures for which it is enough to use the maintenance of internal consistency during learning and further network processing. Owing to the method application these processes will have acceptable computational complexity.

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