Sensitivity Statistical Estimates for Local A Posteriori Inference Matrix-Vector Equations in Algebraic Bayesian Networks over Quantum Propositions
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An approach to the sensitivity analysis of local a posteriori inference equations in algebraic Bayesian networks is proposed in this paper. Some basic definitions and formulations are briefly given and the development of the matrix-vector a posteriori inference approach is considered. Some cases of the propagation of deterministic and stochastic evidence in a knowledge pattern with scalar estimates of component truth probabilities over quantum propositions are described. For each of the considered cases, the necessary metrics are introduced, and some transformations resulting in four linear programming problems are performed. The solution of these problems gives the required estimates. In addition, two theorems postulating the covering estimates for the considered parameters are formulated. The results obtained in this work prove the correct application of models and create a basis for the sensitivity analysis of local and global probabilistic-logic inference equations.
Keywordsuncertain knowledge propagation of evidence probabilistic logic algebraic Bayesian networks probabilistic-logic inference sensitivity statistical estimates probabilistic graphical models matrix-vector equations
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- 2.V. I. Gorodetskii, “Algebraic Bayesian networks — New paradigm of expert systems,” in Jubilee Collection of Works of Institutes of the Department of Informatics, Computer Science and Automation of RAS (Otd. Inf., Vychisl. Tekh. i Avtom. Ross. Akad. Nauk, Moscow, 1993), Vol. 2, pp. 120–141 [in Russian].Google Scholar
- 5.M. W. L. Moreira, J. J. P. C. Rodrigues, A. M. B. Oliveira, R. F. Ramos, and K. Saleem, “A preeclampsia diagnosis approach using Bayesian networks,” in Proc. IEEE Int. Conf. on Communications (ICC), Kuala Lumpur, Malaysia, May 23–27, 2016 (IEEE, Piscataway, NJ, 2016).Google Scholar
- 9.H. M. Nemati, A. Sant’Anna, and S. Nowaczyk, “Bayesian Network representation of meaningful patterns in electricity distribution grids,” in Proc. IEEE Int. Energy Conf., Leuven, Belgium, Apr. 4–8, 2016 (IEEE, Piscataway, NJ, 2016).Google Scholar
- 12.B. Ojeme and A. Mbogho, “Predictive strength of Bayesian networks for diagnosis of depressive disorders”, in Proc. 8th KES Int. Conf. on Intelligent Decision Technologies (KES-IDT 2016), Puerto de la Cruz, Spain, June 15–17, 2016 (Springer-Verlag, Cham, Switzerland, 2016), pp. 373–382.Google Scholar
- 13.N. V. Hovanov, Analysis and Synthesis of Indicators with Information Shortage (S.-Peterb. Gos. Univ., St. Petersburg, 1996) [in Russian].Google Scholar
- 18.A. L. Tulupyev, Bayesian Networks: Probabilistic-Logic Inference in Cycles (S.-Peterb. Gos. Univ., St. Petersburg, 2008) [in Russian].Google Scholar
- 19.A. L. Tulupyev, A. V. Sirotkin, and S. I. Nikolenko, Bayesian Belief Networks: Probabilistic-Logic Inference in Acyclic Directed Graphs (S.-Peterb. Gos. Univ., St. Petersburg, 2009) [in Russian].Google Scholar
- 20.A. L. Tulupyev, S. I. Nikolenko, and A. V. Sirotkin, Bayesian Networks: Probabilistic-Logic Approach (Nauka, St. Petersburg, 2006) [in Russian].Google Scholar
- 21.A. L. Tulupyev and A. V. Sirotkin, “Matrix-vector equations for local probabilistic-logic inference in algebraic Bayesian networks,” Vestn. S.-Peterb. Univ., Ser. 1: Mat., Mekh., Astron., No. 3, 63–72 (2012).Google Scholar
- 22.A. L. Tulupyev and A. V. Sirotkin, “Sensitivity of the results of local a priori and local posteriori inference in algebraic Bayesian networks,” in Proc. Scientific Session of NRNU MEPhI–2010, Moscow, Jan. 25–31, 2010 (NIYaU MIFI, Moscow, 2010), p. 75.Google Scholar