Learning Bayesian Network Parameters from a Small Data Set: A Further Constrained Qualitatively Maximum a Posteriori Method

Journal article


Guo, Zhi-gao, Gao, Xiao-guang, Hao, Ren, Yang, Yu, Di, Ruo-hai and Chen, D (2017). Learning Bayesian Network Parameters from a Small Data Set: A Further Constrained Qualitatively Maximum a Posteriori Method. International Journal of Approximate Reasoning. 91 (Dec), pp. 22-35.
AuthorsGuo, Zhi-gao, Gao, Xiao-guang, Hao, Ren, Yang, Yu, Di, Ruo-hai and Chen, D
Abstract

To improve the learning accuracy of the parameters in a Bayesian network from a small data set, domain knowledge is normally incorporated into the learning process as parameter constraints. MAP-based (Maximum a Posteriori) methods that utilize both sample data and domain knowledge have been well studied in the literature. Among all the MAP-based methods, the QMAP (Qualitatively Maximum a Posteriori) method is one of the algorithms with the highest learning performance. When the data is insufficient, however, the estimation given by the QMAP often fails to satisfy all the parameter constraints, and this has made the overall QMAP estimation unreliable. To ensure that a QMAP estimation does not violate any given parameter constraints and further to improve the learning accuracy, a FC-QMAP (Further Constrained Qualitatively Maximum a Posteriori) algorithm is proposed in this paper. The algorithm regulates QMAP estimation by replacing data estimation with a further constrained estimation via convex optimization. Experiments and theoretical analysis show that the proposed algorithm outperforms most of the existing parameter learning methods including Maximum Likelihood, Constrained Maximum Likelihood, Maximum Entropy, Constrained Maximum Entropy, Maximum a Posteriori, and Qualitatively Maximum a Posteriori.

KeywordsBayesian network; Parameter learning; Small data set; Artificial Intelligence And Image Processing; Domain knowledge
Year2017
JournalInternational Journal of Approximate Reasoning
Journal citation91 (Dec), pp. 22-35
PublisherElsevier BV
ISSN0888-613X
Digital Object Identifier (DOI)doi:10.1016/j.ijar.2017.08.009
Publication dates
Print04 Sep 2017
Publication process dates
Deposited08 Nov 2017
Accepted15 Aug 2017
Accepted author manuscript
License
CC BY-NC-ND 4.0
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https://openresearch.lsbu.ac.uk/item/86xzv

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