TY - JOUR

T1 - Sensitivity Statistical Estimates for Local A Posteriori Inference Matrix-Vector Equations in Algebraic Bayesian Networks over Quantum Propositions

AU - Zolotin, A. A.

AU - Tulupyev, A. L.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - algebraic Bayesian networks

KW - matrix-vector equations

KW - probabilistic graphical models

KW - probabilistic logic

KW - probabilistic-logic inference

KW - propagation of evidence

KW - sensitivity statistical estimates

KW - uncertain knowledge

UR - http://www.scopus.com/inward/record.url?scp=85045026486&partnerID=8YFLogxK

U2 - 10.3103/S1063454118010168

DO - 10.3103/S1063454118010168

M3 - Article

AN - SCOPUS:85045026486

VL - 51

SP - 42

EP - 48

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 1

ER -