Algebraic Bayesian Networks: Using the Canonical Representation of the Knowledge Pattern in Local Inference

The theory of probabilistic graphical models is one of the foundations for studying methods of representing and processing probabilistic dependencies between variables, replacing the need to store all possible joint probability distributions with a graphical representation reflecting conditional dependencies. One of the representation of probabilistic graphical models are algebraic Bayesian networks, in which network nodes represent models of a pattern of knowledge, and edges reflect their relationship. Each element of a knowledge pattern is assigned a probability of truth assessment — scalar or interval. In a situation where knowledge patterns have interval estimates, processing can take a significant amount of time, which may require searching for a canonical representation of a knowledge pattern, i.e. switching from interval estimates to scalar ones. Currently, two methods for constructing a canonical representation are known: a long but accurate method and a fast but approximate method using the Monte Carlo method. This work consists of defining an algorithm for automating the construction of a canonical representation of a knowledge pattern and estimating the error that occurs when using an approximate algorithm in the process of a posteriori inference, which is one of the main ways of using algebraic Bayesian networks and knowledge patterns in practice. In the course of the work, an estimate of the accuracy of the results was found when using an approximate algorithm for knowledge patterns consisting of 1–3 quanta, which amounted to about 0.02 probability assessment units.