Algebraic Bayesian Networks: the Generation of the Knowledge Pattern Canonical Representation

Abstract

Algebraic Bayesian networks relate to the class of probabilistic graphical models. The data in the network is divided into smaller parts - knowledge patterns. Each knowledge pattern can be presented as a quanta set. Each element of the knowledge pattern has a scalar or interval estimates of probability. The handling of networks with scalar estimates has large complexity. This is why one of the tasks during working with Algebraic Bayesian networks with interval estimates is to find the canonical representation of these networks. The canonical representation is the network with scalar estimates, which presents the reduced information from the first one. The task of this study is to generate the canonical representation for a separately taken knowledge pattern. This task is solved with the usage of Monte-Carlo method, approach and algorithm are described, an example of algorithm's usage is shown and a naive approach for generation of the whole network canonical representation is proposed.