Matrix equations for normalizing factors in the local posteriori inferenceof the truth estimation in algebraic Bayesian networks

Authors

  • Aleksey L. Tulupyev St. Petersburg State University, Universitetskaya nab., 7-9, St. Petersburg, 199034, Russian Federation; St.Petersburg Institute for Informatics and Automation RAS, 14-ya liniya V.O., 39, St.Petersburg, 199178, Russian Federation;
  • Aleksandr V. Sirotkin St. Petersburg State University, Universitetskaya nab., 7-9, St. Petersburg, 199034, Russian Federation; St.Petersburg Institute for Informatics and Automation RAS, 14-ya liniya V.O., 39, St.Petersburg, 199178, Russian Federation;
  • Andrey A. Zolotin St. Petersburg State University, Universitetskaya nab., 7-9, St. Petersburg, 199034, Russian Federation;

Abstract

A posteriori inference is one of three kinds of probabilistic-logic inferences, which the processing of fragments of knowledge with probabilistic uncertainty using Bayesian networks is based on. In this paper, the key terms and theorems statements describing local posteriori inference in algebraic Bayesian networks are given in terms of matrix-vector language. The main result is that we managed to construct a matrixvector equation for the normalizing factors, appearing in the formulas of posterior probabilities of quantum and conjuncts ideals. The whole local posterirori inference equations presented in natrix-vector terms simplify specifications of related inference algorithms and make their implementation more transparent as well as open a way to the classical mathematical technique usage for the inference results sensitivity analysis. Refs 14. Tables 1.

Keywords:

probabilistic logic, Bayesian networks, probabilistic-logic inference, normalizing factors, uncertain knowledge, evidence propagation, consistency

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Published

2015-08-01

How to Cite

Tulupyev, A. L., Sirotkin, A. V., & Zolotin, A. A. (2015). Matrix equations for normalizing factors in the local posteriori inferenceof the truth estimation in algebraic Bayesian networks. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2(3), 379–386. Retrieved from https://math-mech-astr-journal.spbu.ru/article/view/11172

Issue

Vol. 2 No. 3 (2015)

Section

Mathematics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.