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

Among probabilistic graphical models, the class of algebraic Bayesian networks stands out. The theory of algebraic Bayesian networks is based on the decomposition of knowledge into knowledge patterns represented as sets of statements. Knowledge patterns are formalized, in particular, by means of their representation as a set of quanta with scalar or interval estimates of truth probability. A distinctive aspect of the practical application of algebraic Bayesian networks is that the work of algorithms with interval estimations takes several orders of magnitude longer than with scalar ones. Therefore, when time or computational resources are scarce, it may be relevant to construct a knowledge pattern with scalar estimates that best characterizes the knowledge pattern with interval estimates, i.e., to construct a canonical representation of the knowledge pattern. Previously, an approach to approximate construction of the canonical representation of the knowledge pattern was proposed, but the exact generation for knowledge patterns of small cardinality can give a gain in time, which is the subject of this paper. It was shown that the algorithm of exact generation in the case of knowledge pattern of cardinality 1 works almost instantaneously, in the case of knowledge pattern of cardinality 2–30 times faster, for cardinality 3 — faster by 1.5–2 times. This approach is all the more relevant because it is the knowledge patterns of small cardinality that are supposed to be used in the practical application of algebraic Bayesian networks.