Approximating credal network inferences by linear programming

Authors:
Alessandro Antonucci;Cassio P. de Campos;David Huber;Marco Zaffalon
Affiliations:
Istituto Dalle Molle di Studi sull'Intelligenza Artificiale (IDSIA), Manno-Lugano, Switzerland;Istituto Dalle Molle di Studi sull'Intelligenza Artificiale (IDSIA), Manno-Lugano, Switzerland;Istituto Dalle Molle di Studi sull'Intelligenza Artificiale (IDSIA), Manno-Lugano, Switzerland;Istituto Dalle Molle di Studi sull'Intelligenza Artificiale (IDSIA), Manno-Lugano, Switzerland
Venue:
ECSQARU'13 Proceedings of the 12th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Year:
2013

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Abstract

An algorithm for approximate credal network updating is presented. The problem in its general formulation is a multilinear optimization task, which can be linearized by an appropriate rule for fixing all the local models apart from those of a single variable. This simple idea can be iterated and quickly leads to very accurate inferences. The approach can also be specialized to classification with credal networks based on the maximality criterion. A complexity analysis for both the problem and the algorithm is reported together with numerical experiments, which confirm the good performance of the method. While the inner approximation produced by the algorithm gives rise to a classifier which might return a subset of the optimal class set, preliminary empirical results suggest that the accuracy of the optimal class set is seldom affected by the approximate probabilities.