Abstract
Bayesian networks (BNs) parameter learning is a challenging task as it relies on a large amount of reliable and representative training data. Unfortunately, it is often difficult to obtain sufficient samples in many real-world applications. Monotonicity, as a class of prior information, widely exist in various practical tasks. This information is helpful for BN parameter learning. However, monotonicity is set by users traditionally. In this paper, we propose a data-dependent BN parameter learning method which can construct monotonicity constraints for BN parameters automatically. Firstly, we introduce rank mutual information (RMI) and Spearman rank correlation coefficient (RHO) to detect monotonicity among network nodes, and then construct monotonicity constraints for BN parameters. Finally, we transform the problem of parameter learning with monotonicity constraints into a convex Lagrange function and obtain the global optimum solution in polynomial time. Experimental results on real-world classification data and standard BNs show the effectiveness of our proposed algorithms with limited data.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Altendorf, E., Restificar, A.C., Dietterich, T.G.: Learning from sparse data by exploiting monotonicity constraints. In: Proceedings of the 21st Conference in Uncertainty in Artificial Intelligence, pp. 18–26 (2005)
Barber, D.: Bayesian Reasoning and Machine Learning. Cambridge University Press, New York (2012)
Cai, B., Huang, L., Xie, M.: Bayesian networks in fault diagnosis. IEEE Trans. Ind. Inform. 13(5), 2227–2240 (2017)
de Campos, C.P., Tong, Y., Ji, Q.: Constrained maximum likelihood learning of Bayesian networks for facial action recognition. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008. LNCS, vol. 5304, pp. 168–181. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-88690-7_13
Constantinou, A.C., Fenton, N.E., et al.: From complex questionnaire and interviewing data to intelligent Bayesian network models for medical decision support. Artif. Intell. Med. 67, 75–93 (2016)
Constantinou, A.C., Freestone, M., et al.: Causal inference for violence risk management and decision support in forensic psychiatry. Decis. Support Syst. 80, 42–55 (2015)
Constantinou, A.C., Yet, B., et al.: Value of information analysis for interventional and counterfactual Bayesian networks in forensic medical sciences. Artif. Intell. Med. 66, 41–52 (2016)
Farid, M.H., Ilyas, I.F., et al.: LONLIES: estimating property values for long tail entities. In: Proceedings of the 39th International ACM SIGIR Conference on Research and Development in Information Retrieval, pp. 1125–1128 (2016)
Feelders, A.J., van der Gaag, L.C.: Learning Bayesian network parameters with prior knowledge about context-specific qualitative influences. In: Proceedings of the 21st Conference in Uncertainty in Artificial Intelligence, pp. 193–200 (2005)
van der Gaag, L.C., Bodlaender, H.L., Feelders, A.J.: Monotonicity in Bayesian networks. In: Proceedings of the 20th Conference in Uncertainty in Artificial Intelligence, pp. 569–576 (2004)
Hu, Q., Guo, M., Yu, D., Liu, J.: Information entropy for ordinal classification. Sci. China Inf. Sci. 53(6), 1188–1200 (2010)
Marvin, H.J.P., Bouzembrak, Y., Janssen, E.M., et al.: Application of Bayesian networks for hazard ranking of nanomaterials to support human health risk assessment. Nanotoxicology 11(1), 123–133 (2017)
Myers, J.L., Well, A.D.: Research Design and Statistical Analysis (Second Edition ed.), 2nd edn. L. Erlbaum Associates, Mahwah (2010)
Niculescu, R.S.: Exploiting parameter domain knowledge for learning in Bayesian networks. Technical Report CMU-TR-05-147. Carnegie Mellon University (2005)
Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Mateo (1988)
Pei, S., Hu, Q., Chen, C.: Multivariate decision trees with monotonicity constraints. Knowl. Based Syst. 112, 14–25 (2016)
Powers, D.M.W.: Applications and explanations of Zipf’s law. Adv. Neural Inf. Process. Syst. 5(4), 595–599 (1998)
Wang, Z., Wang, Z., et al.: Fault detection and diagnosis of chillers using Bayesian network merged distance rejection and multi-source non-sensor information. Appl. Energy 188, 200–214 (2017)
Zhou, Y., et al.: An empirical study of Bayesian network parameter learning with monotonic influence constraints. Decis. Support Syst. 87, 69–79 (2016)
Acknowledgement
This work is partly supported by National Natural Science Foundation of China under Grants 61732011, 61432011 and U1435212.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Yang, J., Wang, Y., Hu, Q. (2018). Monotonicity Extraction for Monotonic Bayesian Networks Parameter Learning. In: Cheng, L., Leung, A., Ozawa, S. (eds) Neural Information Processing. ICONIP 2018. Lecture Notes in Computer Science(), vol 11303. Springer, Cham. https://doi.org/10.1007/978-3-030-04182-3_50
Download citation
DOI: https://doi.org/10.1007/978-3-030-04182-3_50
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-04181-6
Online ISBN: 978-3-030-04182-3
eBook Packages: Computer ScienceComputer Science (R0)