Publication: Extreme Inaccuracies In Gaussian Bayesian Networks
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To evaluate the impact of model inaccuracies over the network’s output, after the evidence propagation, in a Gaussian Bayesian network, a sensitivity measure is introduced. This sensitivity measure is the Kullback–Leibler divergence and yields different expressions depending on the type of parameter to be perturbed, i.e. on the inaccurate parameter. In this work, the behavior of this sensitivity measure is studied when model inaccuracies are extreme,i.e. when extreme perturbations of the parameters can exist. Moreover, the sensitivity measure is evaluated for extreme situations of dependence between the main variables of the network and its behavior with extreme inaccuracies. This analysis is performed to find the effect of extreme uncertainty about the initial parameters of the model in a Gaussian Bayesian network and about extreme values of evidence. These ideas and procedures are illustrated with an example.
J. Pearl, Probabilistic reasoning in intelligent systems, in: Networks of Plausible Inference, Morgan Kaufmann, Palo Alto, 1988. S.L. Lauritzen, Graphical Models, Clarendon Press, Oxford, 1996. D. Heckerman, A tutorial on learning with Bayesian networks, in: M.I. Jordan (Ed.), Learning in Graphical Models, MIT Press, Cambridge, MA, 1998. F.V. Jensen, Bayesian Networks and Decision Graphs, Springer, New York, 2001. K.B. Laskey, Sensitivity analysis for probability assessments in Bayesian networks, IEEE Transactions on Systems, Man, and Cybernetics 25 (6) (1995) 901–909. V.M.H. Coup´e, L.C. van der Gaag, Properties of sensitivity analysis of Bayesian belief networks, Annals of Mathematics and Artificial Intelligence 36 (2002) 323–356. H. Chan, A. Darwiche, A distance measure for bounding probabilistic belief change, International Journal of Approximate Reasoning 38 (2) (2005) 149–174. E. Castillo, U. Kjærulff, Sensitivity analysis in Gaussian Bayesian networks using a symbolic–numerical technique, Reliability Engineering and System Safety 79 (2003) 139–148. M.A. G´omez-Villegas, P. Ma´ın, R. Susi, Sensitivity analysis in Gaussian Bayesian networks using a divergence measure, Communications in Statistics–Theory and Methods 36 (3) (2007) 523–539. E. Castillo, J.M. Guti´errez, A.S. Hadi, Expert Systems and Probabilistic Network Models, Springer-Verlag, New York, 1997. R. Shachter, C. Kenley, Gaussian influence diagrams, Management Science 35 (5) (1989) 527–550. S. Kullback, R.A. Leibler, On information and sufficiency, Annals of Mathematical Statistics 22 (1951) 79–86.