Bayesian Network Model for Learning Arithmetic Concepts

doi:10.23940/ijpe.19.03.p23.939948

Int J Performability Eng ›› 2019, Vol. 15 ›› Issue (3): 939-948.doi: 10.23940/ijpe.19.03.p23.939948

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Bayesian Network Model for Learning Arithmetic Concepts

Yali Lv^{a, b, *}, Tong Jing^a, Yuhua Qian^b, Jiye Liang^b, Jianai Wu^a, and Junzhong Miao^a

a School of Information Management, Shanxi University of Finance and Economics, Taiyuan, 030006, China;
b Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education, Shanxi University, Taiyuan, 030006, China

Submitted on ; Revised on ;
Contact: sxlvyali@126.com
About author:Yali Lv is an associate professor at Shanxi University of Finance & Economics of China. She received her Ph.D. from Tianjin University. Her research interests include probabilistic reasoning, concept learning, data mining, and machine learning.Tong Jing is a master's candidate at Shanxi University of Finance & Economics of China. His research interests include Bayesian machine learning and concept learning. Yuhua Qian is a professor in the Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education at Shanxi University of China. He received his Ph.D. from Shanxi University. His research interests include granular computing, social computing, and machine learning for big data.Jiye Liang is a professor in the Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education at Shanxi University of China. He received his Ph.D. from Xi'an Jiaotong University. His research interests include computational intelligence, granular computing, data mining, and knowledge discovery.Jianai Wu is a master's candidate at Shanxi University of Finance & Economics of China. Her research interests include data mining and financial data analysis. Junzhong Miao is a master's candidate at Shanxi University of Finance & Economics of China. His research interests include Bayesian machine learning and concept learning.

Abstract

Abstract: An object usually belongs to multiple concepts, but some concepts can be judged directly while other concepts need to be inferred indirectly. To learn some arithmetic concepts from positive integer number sets, we address an arithmetic concept Bayesian network (ACBN) model by taking advantage of Bayesian networks. Specifically, we first give an ACBN model to represent the arithmetic concept knowledge and their direct relationships, and then we design an ACBN model learning algorithm based on domain knowledge. Furthermore, to infer indirectly some arithmetic concepts, we design the learning method of evidence concepts based on the idea of k-nearest neighbors, and then we propose the inference algorithm of the ACBN model. Finally, the experimental results demonstrate that the ACBN model can effectively learn some daily arithmetic concepts.

Key words: probabilistic inference, Bayesian networks, arithmetic concepts, evidence concepts, domain knowledge

Yali Lv, Tong Jing, Yuhua Qian, Jiye Liang, Jianai Wu, and Junzhong Miao. Bayesian Network Model for Learning Arithmetic Concepts [J]. Int J Performability Eng, 2019, 15(3): 939-948.

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Bayesian Network Model for Learning Arithmetic Concepts

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