Abstract
Recent years have seen a surge of interest in methods for representing and reasoning with imprecise data. In this paper, we propose a new possibilistic likelihood function handling this particular form of data based on the interpretation of a possibility distribution as a contour function of a random set. The proposed function can serve as the foundation for inferring several possibilistic models. In this paper, we apply it to define a new scoring function to learn possibilistic network structure. Experimental study showing the efficiency of the proposed score is also presented.
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
Notes
- 1.
Used benchmarks are publicly available in: https://sites.google.com/site/karimtabiasite/mappos.
- 2.
Since \(\pi \)K2 handles variables in a predefined order, so, we generate 5 orders in each experiment and we retain the best structure.
References
Ben Amor, N., Benferhat, S.: Graphoid properties of qualitative possibilistic independence relations. Int. J. Uncertainty, Fuzziness Knowl.-Based Syst. 13(01), 59–96 (2005)
Borgelt, C., Kruse, R.: Operations and evaluation measures for learning possibilistic graphical models. Artif. Intell. 148(1), 385–418 (2003)
Chow, C., Liu, C.: Approximating discrete probability distributions with dependence trees. IEEE Trans. Inf. Theory 14(3), 462–467 (1968)
Cooper, G.F., Herskovits, E.: A Bayesian method for the induction of probabilistic networks from data. Mach. Learn. 9(4), 309–347 (1992)
Couso, I., Dubois, D.: Maximum likelihood under incomplete information: toward a comparison of criteria. In: Ferraro, M.B., Giordani, P., Vantaggi, B., Gagolewski, M., Gil, M.Á., Grzegorzewski, P., Hryniewicz, O. (eds.) Soft Methods for Data Science. AISC, vol. 456, pp. 141–148. Springer, Cham (2017). doi:10.1007/978-3-319-42972-4_18
Denoeux, T.: Maximum likelihood estimation from uncertain data in the belief function framework. IEEE Trans. knowl. data Eng. 25(1), 119–130 (2013)
Dubois, D., Prade, H.: Possibility Theory. Springer, Berlin (1988)
Fonck, P.: Propagating uncertainty in a directed acyclic graph. In: Proceedings of the Fourth Information Processing and Management of Uncertainty Conference, 92, 17–20 (1992)
Grünwald, P.D.: Theory and applications: advances in minimum description length, Mdl tutorial (2005)
Haddad, M., Leray, P., Amor, N.B.: Evaluating product-based possibilistic networks learning algorithms. In: Proceedings of Symbolic and Quantitative Approaches to Reasoning with Uncertainty, pp. 312–321 (2015)
Haddad, M., Leray, P., Amor, N.B.: Learning possibilistic networks from data : a survey. In: 16th World Congress of the International Fuzzy Systems Association and the 9th Conference of the European Society for Fuzzy Logic and Technology, pp. 194–201 (2015)
Haddad, M., Leray, P., Levray, A., Tabia, K.: Possibilistic networks parameter learning: Preliminary empirical comparison. In: 8èmes journées francophones de réseaux bayésiens (JFRB 2016), (2016)
Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Francisco (1988)
Rissanen, J.: Modeling by shortest data description. Automatica 14(5), 465–471 (1978)
Sangüesa, R., Cabós, J., Cortes, U.: Possibilistic conditional independence: A similarity-based measure and its application to causal network learning. Int. J. Approximate Reasoning 18(1), 145–167 (1998)
Serrurier, M., Prade, H.: An informational distance for estimating the faithfulness of a possibility distribution, viewed as a family of probability distributions, with respect to data. Int. J. Approximate Reasoning 54(7), 919–933 (2013)
Shafer, G.: A mathematical Theory of Evidence, vol. 1. Princeton University Press, Princeton (1976)
Shapiro, L.G., Haralick, R.M.: A metric for comparing relational descriptions. IEEE Trans. Pattern Anal. Mach. Intell. 1(1), 90–94 (1985)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Haddad, M., Leray, P., Ben Amor, N. (2017). Possibilistic MDL: A New Possibilistic Likelihood Based Score Function for Imprecise Data. In: Antonucci, A., Cholvy, L., Papini, O. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2017. Lecture Notes in Computer Science(), vol 10369. Springer, Cham. https://doi.org/10.1007/978-3-319-61581-3_39
Download citation
DOI: https://doi.org/10.1007/978-3-319-61581-3_39
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-61580-6
Online ISBN: 978-3-319-61581-3
eBook Packages: Computer ScienceComputer Science (R0)