Bayesian Network Reconstruction and Iterative Divergence Problem Solving Method Based on Norm Minimization

Kuo Li^1,*, Aimin Wang¹, Limin Wang¹, Yuetan Zhao¹, Xinyu Zhu²
Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, Changchun, 130012, China
College of Software, Jilin University, Changchun, 130012, China
* Corresponding Author: Kuo Li. Email: email
(This article belongs to the Special Issue: Incomplete Data Test, Analysis and Fusion Under Complex Environments)

Computer Modeling in Engineering & Sciences https://doi.org/10.32604/cmes.2025.061242

Received 20 November 2024; Accepted 19 February 2025; Published online 13 March 2025

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Abstract

A Bayesian network reconstruction method based on norm minimization is proposed to address the sparsity and iterative divergence issues in network reconstruction caused by noise and missing values. This method achieves precise adjustment of the network structure by constructing a preliminary random network model and introducing small-world network characteristics and combines L1 norm minimization regularization techniques to control model complexity and optimize the inference process of variable dependencies. In the experiment of game network reconstruction, when the success rate of the L1 norm minimization model’s existence connection reconstruction reaches 100%, the minimum data required is about 40%, while the minimum data required for a sparse Bayesian learning network is about 45%. In terms of operational efficiency, the running time for minimizing the L1 norm is basically maintained at 1.0 s, while the success rate of connection reconstruction increases significantly with an increase in data volume, reaching a maximum of 13.2 s. Meanwhile, in the case of a signal-to-noise ratio of 10 dB, the L1 model achieves a 100% success rate in the reconstruction of existing connections, while the sparse Bayesian network had the highest success rate of 90% in the reconstruction of non-existent connections. In the analysis of actual cases, the maximum lift and drop track of the research method is 0.08 m. The mean square error is 5.74 cm². The results indicate that this norm minimization-based method has good performance in data efficiency and model stability, effectively reducing the impact of outliers on the reconstruction results to more accurately reflect the actual situation.