Bayesian network parameter learning algorithm based on improved QMAP

被引：0
作者：
Di R. [1 ]
Li Y. [1 ]
Wan K. [2 ]
Lyu Z. [1 ]
Wang P. [1 ]
机构：
[1] School of Electronic and Information Engineering, Xi'an Technological University, Xi'an
[2] School of Electronic and Information, Northwestern Polytechnical University, Xi'an
来源：
Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University | 2021年 / 39卷 / 06期
关键词：
Bayesian network; Objective optimization; Parameter constraints; Parameter learning; Qualitative maximum a posteriori estimation;
D O I：
10.1051/jnwpu/20213961356
中图分类号：
学科分类号：
摘要：
Small data sets make the statistical information in Bayesian network parameter learning inaccurate, which makes it difficult to get accurate Bayesian network parameters based on data. Qualitative maximum a posteriori estimation (QMAP) is the most accurate algorithm for Bayesian network parameter learning under the condition of small data sets. However, when the number of parameter constraints is large or the parameter feasible region is small, the rejection-acceptance sampling process in QMAP algorithm will become extremely time-consuming. In order to improve the learning efficiency of QMAP algorithm and not affect its learning accuracy as much as possible, a new analytical calculation method of the center point of constrained region is designed to replace the original rejection-acceptance sampling calculation method. Firstly, a new objective function is designed, and a constrained objective optimization problem for solving the boundary points of the constrained region is constructed. Secondly, a new optimization engine is used to solve the objective optimization problem, and the boundary points and center points of the constrained region are obtained. Finally, the existing QMAP algorithm is improved by the obtained center points. The simulation results show that the CMAP algorithm proposed in this paper has a slightly worse parameter learning accuracy than the QMAP algorithm, but its computational efficiency is 2-5 times higher than that of the QMAP algorithm. © 2021 Journal of Northwestern Polytechnical University.
引用
收藏
页码：1356 / 1367
页数：11
相关论文
共 18 条
[1]  
WITTIG F, JAMESON A., Exploiting qualitative knowledge in the learning of conditional probabilities of Bayesian networks, Proceedings of the Sixteenth International Conference on Uncertainty in Artificial Intelligence, (2000)
[2]  
FEELDERS A, GAAG L., Learning Bayesian network parameters under order constraints, International Journal of Approximate Reasoning, 42, 1, pp. 37-53, (2006)
[3]  
MASEGOSA A R, FEELDERS A J, GAAG L C V D., Learning from incomplete data in Bayesian networks with qualitative influences, International Journal of Approximate Reasoning, 69, pp. 18-34, (2016)
[4]  
MARTIN Plajner, JIRIVomlel, Learning bipartite Bayesian networks under monotonicity restrictions, International Journal of General Systems, 49, 1, pp. 88-111, (2020)
[5]  
ZHOU Y, FENTON N, ZHU C., An empirical study of Bayesian network parameter learning with monotonic influence constraints, Decision Support Systems, 87, pp. 69-79, (2016)
[6]  
DI Ruohai, GAO Xiaoguang, GUO Zhigao, Parameter learning of discrete Bayesian networks based on monotonicity constraints, Systems Engineering and Electronics, 18, 5, pp. 272-277, (2014)
[7]  
DI Ruohai, GAO Xiaoguang, GUO Zhigao, Learning Bayesian networks parameters under new monotonic constraints, Journal of Systems Engineering and Electronics, 28, 6, pp. 1248-1255, (2017)
[8]  
REN Jia, GAO Xiaoguang, BAI Yong, Discrete DBN parameter learning under the condition of incomplete information with small samples, Systems Engineering and Electronics, 34, 8, pp. 1723-1728, (2012)
[9]  
ZENG Qiang, HUANG Zheng, WEI Shuhuan, Bayesian network parameter learning method based on expert prior knowledge and monotonicity constraint, Systems Engineering and Electronics, 42, 3, pp. 642-656, (2020)
[10]  
NICULESCU R, MITCHELL T, RAO B., Bayesian network learning with parameter constraints, Journal of Machine Learning Research, 7, 1, pp. 1357-1383, (2006)
12