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

Among probabilistic graphical models we can distinguish a class of algebraic Bayesian networks defined over structurally smaller objects — mathematical models of knowledge patterns (KPs). The KPs themselves store closely related information about the subject domain, which is formalised, in particular, as a set of quanta with scalar or interval estimates of the probability of truth. When computational and time resources are scarce, it can be useful to search for a canonical representation of the KP — moving from objects with interval estimates to the most representative objects with scalar estimates. Previously, an algorithm for finding an approximate canonical representation of a KP was proposed, using a Monte Carlo method and looking for the average between a large number of KPs with scalar estimates. This paper considers a refinement of this algorithm by replacing the gamma distribution, which was used to generate the scalar estimates, with an exponential distribution. As a result, it was experimentally shown that the canonical representations of KPs obtained in this case are generated 8 times more accurately.