Possibilistic networks parameter learning: Preliminary empirical comparison

International audienceLike Bayesian networks, possibilistic ones compactly encode joint uncertainty representations over a set of variables. Learning possibilistic networks from data in general and from imperfect or scarce data in particular, has not received enough attention. Indeed, only few works deal with learning the structure and the parameters of a possibilistic network from a dataset. This paper provides a preliminary comparative empirical evaluation of two approaches for learning the parameters of a possibilistic network from empirical data. The first method is a possibilistic approach while the second one first learns imprecise probability measures then transforms them into possibility distributions by means of probability-possibility transformations. The comparative evaluation focuses on learning belief networks on datasets with missing data and scarce datasets

A complexity analysis of MPE inference in possibilistic networks

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Probability-Possibility Transformations: Application to Credal Networks

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On the Analysis of Probability-Possibility Transformations: Changing Operations and Graphical Models

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Approximation de l’inférence MAP via les transformations probabilistes-possibilistes

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Possibilistic Networks: Computational Analysis of MAP and MPE Inference

International audiencePossibilistic graphical models are powerful modeling and reasoning tools for uncertain information based on possibility theory. In this paper, we provide an analysis of computational complexity of MAP and MPE queries for possibilistic networks. MAP queries stand for maximum a posteriori explanation while MPE ones stand for most plausible explanation. We show that the decision problems of answering MAP and MPE queries in both min-based and product-based possibilistic networks is NP-complete. Definitely, such results represent an advantage of possibilistic graphical models over probabilistic ones since MAP queries are NP PP -complete in Bayesian networks. Our proofs for querying min-based possibilistic networks make use of reductions from the 3SAT problem to querying possibilistic networks decision problem. Moreover, the provided reductions may be useful for the implementation of MAP and MPE inference engines based on the satisfiability problem solvers. As for product-based networks, the provided proofs are incremental and make use of reductions from SAT and its weighted variant WMAXSAT

Approximating MAP inference in credal networks using probability-possibility transformations

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Set-Valued Conditioning in a Possibility Theory Setting

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Learning the parameters of possibilistic networks from data: Empirical comparison

International audiencePossibilistic networks are belief graphical models based on possibility theory. A possibilistic network either represents experts' epistemic uncertainty or models uncertain information from poor, scarce or imprecise data. Learning possibilistic networks from data in general and from imperfect or scarce datasets in particular, has not received enough attention. This work focuses on parameter learning of possibilistic networks. The main contributions of the paper are i) a study of an extension of the information affinity measure to assess the similarity of possibilistic networks and ii) a comparative empirical evaluation of two approaches for learning the parameters of a possibilistic network from empirical data

Compatible-Based Conditioning in Interval-Based Possibilistic Logic

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