Approximating credal network inferences by linear programming

Antonucci, Alessandro and De Campos, Cassio Polpo and Huber, David and Zaffalon, Marco (2013) Approximating credal network inferences by linear programming. In: The 12th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, 7-10 July 2013, Utrecht University: Utrecht, The Netherlands.

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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.

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