Abstract
Bayesian network classifiers are widely used in machine learning because they intuitively represent causal relations. Multi-label classification problems require each instance to be assigned a subset of a defined set of h labels. This problem is equivalent to finding a multi-valued decision function that predicts a vector of h binary classes. In this paper we obtain the decision boundaries of two widely used Bayesian network approaches for building multi-label classifiers: Multi-label Bayesian network classifiers built using the binary relevance method and Bayesian network chain classifiers. We extend our previous single-label results to multi-label chain classifiers, and we prove that, as expected, chain classifiers provide a more expressive model than the binary relevance method.
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References
Bielza, C., Larrañaga, P.: Discrete Bayesian network classifier: A survey. ACM Computing Surveys 47(1) (in press, 2015)
Bielza, C., Li, G., Larrañaga, P.: Multi-dimensional classification with Bayesian networks. International Journal of Approximate Reasoning 52, 705–727 (2011)
Borchani, H., Bielza, C., Larrañaga, P.: Learning CB-decomposable multi-dimensional Bayesian network classifiers. In: Petri, M., Teemu, R., Tommi, J. (eds.) Proceedings of the 5th European Workshop on Probabilistic Graphical Models (PGM 2010), pp. 25–32. HIIT Publications (2010)
van der Gaag, L.C., de Waal, P.R.: Multi-dimensional Bayesian network classifiers. In: Studený, M., Vomlel, J. (eds.) Third European Workshop on Probabilistic Graphical Models, pp. 107–114 (2006)
Friedman, N., Geiger, D., Goldszmidt, M.: Bayesian network classifiers. Machine Learning 29(2-3), 131–163 (1997)
Godbole, S., Sarawagi Discriminative, S.: methods for multi-labeled classification. In: Advances in Knowledge Discovery and Data Mining, pp. 22–30. Springer (2004)
Kelner, R., Lerner, B.: Learning bayesian network classifiers by risk minimization. International Journal of Approximate Reasoning 53(2), 248–272 (2012)
Keogh, E.J., Pazzani Learning, M.J.: the structure of augmented Bayesian classifiers. International Journal on Artificial Intelligence Tools 11(04), 587–601 (2002)
Minsky, M.: Steps toward artificial intelligence. In: Computers and Thought, pp. 406–450. McGraw-Hill (1961)
Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann Publishers Inc. (1988)
Peot, M.A.: Geometric implications of the naive Bayes assumption. In: Eric, H., Finn, J. (eds.) Proceedings of the Twelfth International Conference on Uncertainty in Artificial Intelligence, pp. 414–419. Morgan Kaufmann Publishers Inc (1996)
de Waal, P.R., van der Gaag, L.C.: Inference and Learning in Multi-dimensional Bayesian Network Classifiers. In: Mellouli, K. (ed.) ECSQARU 2007. LNCS (LNAI), vol. 4724, pp. 501–511. Springer, Heidelberg (2007)
Read, J., Bielza, C., Larrañaga, P.: Multi-dimensional classification with super-classes. IEEE Transactions on Knowledge and Data Engineering (2013)
Read, J., Pfahringer, B., Holmes, G., Frank, E.: Classifier Chains for Multi-label Classification. In: Buntine, W., Grobelnik, M., Mladenić, D., Shawe-Taylor, J. (eds.) ECML PKDD 2009, Part II. LNCS, vol. 5782, pp. 254–269. Springer, Heidelberg (2009)
Sucar, L.E., Bielza, C., Morales, E.F., Hernandez-Leal, P., Zaragoza, J.H., Larrañaga, P.: Multi-label classification with Bayesian network-based chain classifiers. Pattern Recognition Letter 41, 14–22 (2014)
Vapnik, V.N.: The Nature of Statistical Learning Theory. Springer (1995)
Vapnik, V.N., Chervonenkis, A.: On the uniform convergence of relative frequencies of events to their probabilities. Theory of Probability and Its Applications 16(2), 264–280 (1971)
Varando, G., Bielza, C., Larrañaga, P.: Decision boundary for discrete Bayesian network classifiers. Technical Report UPM-ETSIINF/DIA/2014-1, Universidad Politecnica de Madrid (2014), http://oa.upm.es/26003/
Zhang, M.-L., Zhou, Z.-H.: A review on multi-label learning algorithms. IEEE Transactions on Knowledge and Data Engineering (in press, 2014)
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Varando, G., Bielza, C., Larrañaga, P. (2014). Expressive Power of Binary Relevance and Chain Classifiers Based on Bayesian Networks for Multi-label Classification. In: van der Gaag, L.C., Feelders, A.J. (eds) Probabilistic Graphical Models. PGM 2014. Lecture Notes in Computer Science(), vol 8754. Springer, Cham. https://doi.org/10.1007/978-3-319-11433-0_34
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DOI: https://doi.org/10.1007/978-3-319-11433-0_34
Publisher Name: Springer, Cham
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