Propagation Computation for Mixed Bayesian Networks Using Minimal Strong Triangulation

Yao Liu, Shuai Wang, Can Zhou and Xiaofei Wang ()
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Yao Liu: Key Laboratory for Applied Statistics of MOE and School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
Shuai Wang: Key Laboratory for Applied Statistics of MOE and School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
Can Zhou: School of Statistics and Data Science, Nanjing Audit University, Nanjing 211815, China
Xiaofei Wang: Key Laboratory for Applied Statistics of MOE and School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China

Mathematics, 2024, vol. 12, issue 13, 1-13

Abstract: In recent years, mixed Bayesian networks have received increasing attention across various fields for probabilistic reasoning. Though many studies have been devoted to propagation computation on strong junction trees for mixed Bayesian networks, few have addressed the construction of appropriate strong junction trees. In this work, we establish a connection between the minimal strong triangulation for marked graphs and the minimal triangulation for star graphs. We further propose a minimal strong triangulation method for the moral graph of mixed Bayesian networks and develop a polynomial-time algorithm to derive a strong junction tree from this minimal strong triangulation. Moreover, we also focus on the propagation computation of all posteriors on this derived strong junction tree. We conducted multiple numerical experiments to evaluate the performance of our proposed method, demonstrating significant improvements in computational efficiency compared to existing approaches. Experimental results indicate that our minimal strong triangulation approach provides a robust framework for efficient probabilistic inference in mixed Bayesian networks.

Keywords: Bayesian networks; strong junction trees; propagation computation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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