Probability-Possibility Transformations: Application to Credal Networks

This paper deals with belief graphical models and probability-possibility transformations. It first analyzes some properties of transforming a credal network into a possibilistic one. In particular, we are interested in satisfying some properties of probability-possibility transformations like dominance and order preservation. The second part of the paper deals with using probability-possibility transformations in order to perform MAP inference in credal networks. This problem is known for its high computational complexity in comparison with MAP inference in Bayesian and possibilistic networks. The paper provides preliminary experimental results comparing our approach with both exact and approximate inference in credal networks.

[1]  Adnan Darwiche,et al.  Modeling and Reasoning with Bayesian Networks , 2009 .

[2]  T. Sudkamp.  On probability-possibility transformations , 1992 .

[3]  Nahla Ben Amor,et al.  Probability-Possibility Transformation: - Application to Bayesian and Possibilistic Networks , 2013, WILF.

[4]  Didier Dubois,et al.  Random sets and fuzzy interval analysis , 1991 .

[5]  Anton Wallner.  Extreme points of coherent probabilities in finite spaces , 2007, Int. J. Approx. Reason..

[6]  Didier Dubois,et al.  Transforming Probability Intervals into Other Uncertainty Models , 2007, EUSFLAT Conf..

[7]  Christian Borgelt,et al.  Learning possibilistic graphical models from data , 2003, IEEE Trans. Fuzzy Syst..

[8]  Salem Benferhat,et al.  On the Analysis of Probability-Possibility Transformations: Changing Operations and Graphical Models , 2015, ECSQARU.

[9]  Didier Dubois,et al.  Possibility Theory - An Approach to Computerized Processing of Uncertainty , 1988 .

[10]  Patrick Maher.  Book Review:The Enterprise of Knowledge: An Essay on Knowledge, Credal Probability, and Chance Isaac Levi , 1984 .

[11]  Peter Walley,et al.  Towards a unified theory of imprecise probability , 2000, Int. J. Approx. Reason..

[12]  Thierry Denoeux,et al.  Inferring a possibility distribution from empirical data , 2006, Fuzzy Sets Syst..

[13]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[14]  Fabio Gagliardi Cozman,et al.  Credal networks , 2000, Artif. Intell..

[15]  George J. Klir,et al.  Information-Preserving Probability-Possibility Transformations: , 1993 .

[16]  William L. Harper.  The Enterprise of Knowledge: An Essay on Knowledge, Credal Probability and Chance by Isaac Levi , 1983 .

[17]  Didier Dubois,et al.  Probability-Possibility Transformations, Triangular Fuzzy Sets, and Probabilistic Inequalities , 2004, Reliab. Comput..

[18]  Denis Deratani Mauá,et al.  Probabilistic Inference in Credal Networks: New Complexity Results , 2014, J. Artif. Intell. Res..