Abstract
One recent focus of research in graphical models is how to learn them from imperfect data. Most of existing works address the case of missing data. In this paper, we are interested by a more general form of imperfection i.e. related to possibilistic datasets where some attributes are characterized by possibility distributions. We propose a structural learning method of Directed Acyclic Graphs (DAGs), which form the qualitative component of several graphical models, from possibilistic datasets. Experimental results show the efficiency of the proposed method even in the particular case of missing data regarding the state of the art Closure under tuple intersection (CUTS) method [1].
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
Borgelt, C., Steinbrecher, M., Kruse, R.: Graphical models: representations for learning, reasoning and data mining, vol. 704. Wiley (2009)
Pearl, J.: Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann (1988)
Lauritzen, S.: The EM algorithm for graphical association models with missing data. Computational Statistics & Data Analysis 19(2), 191–201 (1995)
Haouari, B., Ben Amor, N., Elouedi, Z., Mellouli, K.: Naïve possibilistic network classifiers. Fuzzy Sets and Systems 160(22), 3224–3238 (2009)
Bounhas, M., Mellouli, K., Prade, H., Serrurier, M.: From Bayesian classifiers to possibilistic classifiers for numerical data. In: Deshpande, A., Hunter, A. (eds.) SUM 2010. LNCS, vol. 6379, pp. 112–125. Springer, Heidelberg (2010)
Jenhani, I., Amor, N., Elouedi, Z.: Decision trees as possibilistic classifiers. International Journal of Approximate Reasoning 48(3), 784–807 (2008)
Ammar, A., Elouedi, Z., Lingras, P.: K-modes clustering using possibilistic membership. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds.) IPMU 2012, Part III. CCIS, vol. 299, pp. 596–605. Springer, Heidelberg (2012)
Fonck, P.: Propagating uncertainty in a directed acyclic graph. In: IPMU, vol. 92, pp. 17–20 (1992)
Ayachi, R., Ben Amor, N., Benferhat, S., Haenni, R.: Compiling possibilistic networks: Alternative approaches to possibilistic inference. In: Proceedings of the Twenty-Sixth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI 2010), Corvallis, Oregon, pp. 40–47. AUAI Press (2010)
Dubois, D., Prade, H., Harding, E.: Possibility theory: an approach to computerized processing of uncertainty, vol. 2. Plenum Press, New York (1988)
Chow, C., Liu, C.: Approximating discrete probability distributions with dependence trees. IEEE Transactions on Information Theory 14(3), 462–467 (1968)
Cooper, G., Herskovits, E.: A Bayesian method for the induction of probabilistic networks from data. Machine Learning 9(4), 309–347 (1992)
Shannon, E.: A mathematical theory of evidence: Bellsyt. Techn. Journal 27, 379–423 (1948)
Chernoff, H., Lehmann, E.: The use of maximum likelihood estimates in χ 2 tests for goodness of fit. The Annals of Mathematical Statistics 25(3), 579–586 (1954)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this paper
Cite this paper
Haddad, M., Ben Amor, N., Leray, P. (2013). Imputation of Possibilistic Data for Structural Learning of Directed Acyclic Graphs. In: Masulli, F., Pasi, G., Yager, R. (eds) Fuzzy Logic and Applications. WILF 2013. Lecture Notes in Computer Science(), vol 8256. Springer, Cham. https://doi.org/10.1007/978-3-319-03200-9_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-03200-9_8
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-03199-6
Online ISBN: 978-3-319-03200-9
eBook Packages: Computer ScienceComputer Science (R0)