Abstract
In this paper, we propose a Credal EM (CrEM) approach for partially supervised learning. The uncertainty is represented by belief functions as understood in the transferable belief model (TBM). This model relies on a non probabilistic formalism for representing and manipulating imprecise and uncertain information. We show how the EM algorithm can be applied within the TBM framework when applied for the classification of objects and when the learning set is imprecise (the actual class of each object is only known as belonging to a subset of classes), and/or uncertain (the knowledge about the actual class is represented by a probability function or by a belief function).
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
Preview
Unable to display preview. Download preview PDF.
References
Ambroise, C., Denoeux, T., Govaert, G., Smets, P.: Learning from an imprecise teacher: probabilistic and evidential approaches. In: Proceedings of asmda 2001, vol. 1, pp. 100–105. Compiègne, France (2001)
Ambroise, C., Govaert, G.: EM algorithm for partially known labels. In: Proceeding of IFCS 2000, Namur, Belgium, vol. 1 (2000)
Delmotte, F., Smets, P.: Target identification based on the transferable belief model interpretation of Dempster-Shafer model. IEEE Transactions on Systems, Man and Cybernetics, A 34, 457–471 (2004)
Dempster, A., Laird, N., Rubin, D.: Maximum likelihood estimation from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, series B, 39, 1-38 (1977)
Denoeux, T.: A k-nearest neighbor classification rule based on Dempster-Shafer theory. IEEE Transactions on Systems, Man and Cybernetics 25(5), 804–813 (1995)
Denoeux, T., Zouhal, L.M.: Handling possibilistic labels in pattern classification using evidential reasoning. Fuzzy Sets and Systems 122, 47–62 (2001)
Figueiredo, M.A.T., Jain, A.K.: Unsupervised learning of finite mixture models. IEEE Trans. Pattern Anal. Mach. Intell. 24(3), 381–396 (2002)
Hastie, T., Tibshirani, R.J.: Discriminant analysis by gaussian mixtures. Journal of the Royal Statistical Society B 58, 155–176 (1996)
Kennes, R.: Computational aspects of the Möbius transform of a graph. IEEE SMC 22, 201–223 (1992)
McLaclan, G.J., Krishnan, T.: The EM algorithm and extensions. John Wiley, New York (1997)
Smets, P.: Belief functions: the disjunctive rule of combination and the generalized Bayesian theorem. Int. J. Approximate Reasoning 9, 1–35 (1993)
Smets, P.: The transferable belief model for quantified belief representation. In: Gabbay, D.M., Smets, P. (eds.) Handbook of defeasible reasoning and uncertainty management systems, vol. 1, pp. 267–301. Kluwer, Doordrecht (1998)
Smets, P.: Decision making in the TBM: the necessity of the pignistic transformation. Int. J. Approximate Reasoning 38, 133–147 (2005)
Smets, P., Kennes, R.: The transferable belief model. Artificial Intelligence 66, 191–234 (1994)
Zouhal, L.M., Denoeux, T.: An evidence theoretic k-nn rule with parameter optimisation. IEEE Transactions on Systems, Man and Cybernetics - Part C 28, 263–271 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Vannoorenberghe, P., Smets, P. (2005). Partially Supervised Learning by a Credal EM Approach. In: Godo, L. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2005. Lecture Notes in Computer Science(), vol 3571. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11518655_80
Download citation
DOI: https://doi.org/10.1007/11518655_80
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-27326-4
Online ISBN: 978-3-540-31888-0
eBook Packages: Computer ScienceComputer Science (R0)