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Minimizing Regret in Dynamic Decision Problems Read chapter Read first chapter

2015 | OriginalPaper | Chapter

Balanced Tuning of Multi-dimensional Bayesian Network Classifiers

Authors : Janneke H. Bolt, Linda C. van der Gaag

Published in: Symbolic and Quantitative Approaches to Reasoning with Uncertainty

Publisher: Springer International Publishing

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Abstract

Multi-dimensional classifiers are Bayesian networks of restricted topological structure, for classifying data instances into multiple classes. We show that upon varying their parameter probabilities, the graphical properties of these classifiers induce higher-order sensitivity functions of restricted functional form. To allow ready interpretation of these functions, we introduce the concept of balanced sensitivity function in which parameter probabilities are related by the odds ratios of their original and new values. We demonstrate that these balanced functions provide a suitable heuristic for tuning multi-dimensional Bayesian network classifiers, with guaranteed bounds on the changes of all output probabilities.

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previous chapter Multi-classifiers of Small Treewidth
next chapter A New View of Conformity and Its Application to Classification
Appendix
Available only for authorised users
Footnotes
1
In earlier research, we introduced the related concept of sliced sensitivity function [3] which specifies an output probability of a Bayesian network in n linearly related parameters.
 
Literature
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2.
De Bock, J., de Campos, C.P., Antonucci, A.: Global sensitivity analysis for MAP inference in graphical models. In: Ghahramani, Z., Welling, M., Cortes, C., Lawrence, N.D., Weinberger, K.Q. (eds.) Advances in Neural Information Processing Systems, vol. 27, pp. 2690–2698 (2014)
3.
Bolt, J.H., Renooij, S.: Local sensitivity of Bayesian networks to multiple parameter shifts. In: van der Gaag, L.C., Feelders, A.J. (eds.) PGM 2014. LNCS, vol. 8754, pp. 65–80. Springer, Switzerland (2014)
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Borchani, H., Bielza, C., Toro, C., Larrañaga, P.: Predicting human immunodeficiency virus inhibitors using multi-dimensional Bayesian network classifiers. Artif. Intell. Med. 57, 219–229 (2013)CrossRef
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van der Gaag, L.C., de Waal, P.R.: Multi-dimensional Bayesian network classifiers. In: Vomlel, J., Studený, M. (eds.) Proceedings of the Third European Workshop in Probabilistic Graphical Models, pp. 107–114 (2006)
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Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann Publishers, Palo Alto (1988)MATH
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Renooij, S.: Co-variation for sensitivity analysis in Bayesian networks: properties, consequences and alternatives. Int. J. Approximate Reasoning 55, 1022–1042 (2014)MathSciNetCrossRefMATH
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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) CrossRef
Metadata
Title
Balanced Tuning of Multi-dimensional Bayesian Network Classifiers
Authors
Janneke H. Bolt
Linda C. van der Gaag
Copyright Year
2015
Book
Symbolic and Quantitative Approaches to Reasoning with Uncertainty

Print ISBN: 978-3-319-20806-0

Electronic ISBN: 978-3-319-20807-7

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-20807-7_19

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