Algebraic Bayesian Network Secondary Structure Cycles Elimination Based on its Quaternary Structure Analysis

Algebraic Bayesian Network (ABN) is one of the logical and probabilistic graphical models of bases of knowledge patterns uncertainty. Algorithms for global logical and probabilistic inference in ABN can be applied only under the condition of acyclicity of its secondary structure — join graph. The existing method for join graph transformation into join tree application is restrictedly applicable. The goal of the work is to offer new methods for the transformation cyclic ABN into an acyclic one, based on a structure theorem for minimal join graphs cycles. Two methods for eliminating cycles are proposed and their correctness.is proved.