Approximating Credal Network Inferences by Linear Programming
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.
Unable to display preview. Download preview PDF.
- 2.Antonucci, A., de Campos, C.P.: Decision making by credal nets. In: Proceedings of the International Conference on Intelligent Human-Machine Systems and Cybernetics (IHMSC 2011), vol. 1, pp. 201–204. IEEE (2011)Google Scholar
- 6.da Rocha, J.C.F., Cozman, F.G., de Campos, C.P.: Inference in polytrees with sets of probabilities. In: UAI 2003, pp. 217–224 (2003)Google Scholar
- 7.de Campos, C.P., Cozman, F.G.: Inference in credal networks using multilinear programming. In: Proceedings of the Second Starting AI Researcher Symposium, pp. 50–61. IOS Press, Amsterdam (2004)Google Scholar
- 8.de Campos, C.P., Cozman, F.G.: The inferential complexity of Bayesian and credal networks. In: Proceedings of the International Joint Conference on Artificial Intelligence, Edinburgh, pp. 1313–1318 (2005)Google Scholar
- 9.de Campos, C.P., Cozman, F.G.: Inference in credal networks through integer programming. In: International Symposium on Imprecise Probability: Theories and Applications (ISIPTA), Prague, pp. 145–154 (2007)Google Scholar
- 11.Koller, D., Friedman, N.: Probabilistic Graphical Models: Principles and Techniques. MIT Press (2009)Google Scholar
- 13.Mauà, D.D., de Campos, C.P., Zaffalon, M.: Updating credal networks is approximable in polynomial time. Int. J. Approx. Reasoning (2012)Google Scholar
- 14.Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press (1976)Google Scholar
- 15.Walley, P.: Statistical Reasoning with Imprecise Probabilities. Chapman and Hall (1991)Google Scholar