×

Propagation effects of model-calculated probability values in Bayesian networks. (English) Zbl 1343.68245

Summary: Probabilistic causal interaction models have become quite popular among Bayesian-network engineers as elicitation of all probabilities required often proves the main bottleneck in building a real-world network with domain experts. The best-known interaction models are the noisy-OR model and its generalisations. These models in essence are parameterised conditional probability tables for which just a limited number of parameter probabilities are required. The models assume specific properties of intercausal interaction and cannot be applied uncritically. Given their clear engineering advantages however, they are subject to ill-considered use. This paper demonstrates that such ill-considered use can result in poorly calibrated output probabilities from a Bayesian network. By studying, in an analytical way, the propagation effects of noisy-OR calculated probability values, we identify conditions under which use of the model can be harmful for a network’s performance. These conditions demonstrate that use of the noisy-OR model for mere pragmatic reasons is sometimes warranted, even when the model’s underlying assumptions are not met in reality.

MSC:

68T37 Reasoning under uncertainty in the context of artificial intelligence
68T05 Learning and adaptive systems in artificial intelligence
Full Text: DOI

References:

[1] Anand, V.; Downs, S. M., Probabilistic asthma case finding: a noisy-OR reformulation, (AMIA Annual Symposium Proceedings (2008)), 6-10
[2] Bolt, J.; van der Gaag, L. C., An empirical study of the use of the noisy-OR model in a real-life Bayesian network, (Hüllermeier, E.; Kruse, R.; Hoffmann, F., Information Processing and Management of Uncertainty in Knowledge-Based Systems. Information Processing and Management of Uncertainty in Knowledge-Based Systems, Theory and Methods, vol. 80 (2010), Springer: Springer Berlin), 11-20 · Zbl 1209.68532
[3] Castillo, E.; Gutiérrez, J. M.; Gadi, A. S., Sensitivity analysis in discrete Bayesian networks, IEEE Trans. Syst. Man Cybern., 27, 412-423 (1997)
[4] Cooper, G. F., The computational complexity of probabilistic inference using Bayesian belief networks, Artif. Intell., 42, 393-405 (1990) · Zbl 0717.68080
[5] Coupé, V. M.H.; van der Gaag, L. C.; Habbema, J. D.F., Sensitivity analysis: an aid for belief-network quantification, Knowl. Eng. Rev., 15, 215-232 (2000) · Zbl 0988.68186
[6] Coupé, V. M.H.; van der Gaag, L. C., Properties of sensitivity analysis of Bayesian belief networks, Ann. Math. Artif. Intell., 36, 323-356 (2002) · Zbl 1015.68187
[7] Darwiche, A., Modeling and Reasoning with Bayesian Networks (2009), Cambridge University Press: Cambridge University Press Cambridge · Zbl 1231.68003
[8] Díez, F. J., Parameter adjustment in Bayes networks. The generalized noisy-OR gate, (Heckerman, D., Proceedings of the 9th Conference on Uncertainty in Artificial Intelligence (UAI-01) (2001), Morgan Kaufmann Publishers), 165-182
[9] Díez, F. J.; Druzdzel, M. J., Canonical probabilistic models for knowledge engineering (2006), UNED: UNED Madrid, Spain, Technical Report CISIAD-06-01
[10] Druzdzel, M. J.; van der Gaag, L. C., Building probabilistic networks: where do the numbers come from? Guest editors introduction, IEEE Trans. Knowl. Data Eng., 12, 481-486 (2000)
[11] van der Gaag, L. C.; Renooij, S.; Coupé, V. M.H., Sensitivity analysis of probabilistic networks, (Lucas, P.; Gámez, J. A.; Salmeron, A., Advances in Probabilistic Graphical Models. Advances in Probabilistic Graphical Models, Studies in Fuzziness and Soft Computing, vol. 213 (2007), Springer: Springer Berlin), 103-124 · Zbl 1117.90068
[12] van der Gaag, L. C.; Renooij, S.; Witteman, C. L.M.; Aleman, B. M.P.; Taal, B. G., Probabilities for a probabilistic network: a case study in oesophageal cancer, Artif. Intell. Med., 25, 123-148 (2002)
[13] Heckerman, D.; Breese, J., Causal independence for probabilistic assessment and inference using Bayesian networks, IEEE Trans. Syst. Man Cybern., 26, 826-831 (1996)
[14] Henrion, M., Some practical issues in constructing belief networks, (Lemmer, J.; Levitt, T.; Kanal, L., Proceedings of the Third Annual Conference on Uncertainty in Artificial Intelligence (UAI-87) (1987), Elsevier), 161-174
[15] Jensen, F. V.; Nielsen, Th. D., Bayesian Networks and Decision Graphs (2007), Springer Verlag: Springer Verlag New York · Zbl 1277.62007
[16] Koller, D.; Friedman, N., Probabilistic Graphical Models. Principles and Techniques (2009), The MIT Press: The MIT Press Cambridge · Zbl 1183.68483
[17] Kuter, U.; Nau, D.; Gossink, D.; Lemmer, J. F., Interactive course-of-action planning using causal models, (Pechoucek, M.; Tate, A., Proceedings of the Third International Conference on Knowledge Systems for Coalition Operations (KSCO-2004). Proceedings of the Third International Conference on Knowledge Systems for Coalition Operations (KSCO-2004), Prague (2004)), 37-51
[18] Lauritzen, S. L.; Spiegelhalter, D. J., Local computations with probabilities on graphical structures and their application to expert systems, J. R. Stat. Soc. B, 50, 157-224 (1988) · Zbl 0684.68106
[19] Lemmer, J. F.; Gossink, D. E., Recursive noisy OR - a rule for estimating complex probabilistic interactions, IEEE Trans. Syst. Man Cybern., Part B, Cybern., 34, 2252-2261 (2004)
[20] Lucas, P. J.F., Bayesian network modelling through qualitative patterns, Artif. Intell., 163, 233-263 (2005) · Zbl 1132.68772
[21] Ma, J., Qualitative approach to Bayesian networks with multiple causes, IEEE Trans. Syst. Man Cybern., 42, 382-391 (2012)
[22] Morgan, M. G.; Henrion, M., Uncertainty, a Guide to Dealing with Uncertainty in Quantitative Risk and Policy Analysis (1990), Cambridge University Press: Cambridge University Press Cambridge
[23] Oniśko, A.; Druzdzel, M. J.; Wasyluk, H., Learning Bayesian network parameters from small data sets: application of noisy-OR gates, Int. J. Approx. Reason., 27, 165-182 (2001) · Zbl 0988.68827
[24] Parsons, S., Qualitative Methods for Reasoning under Uncertainty (2001), MIT Press · Zbl 0998.68178
[25] Pearl, J., Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference (1988), Morgan Kaufmann Publishers: Morgan Kaufmann Publishers San Francisco
[26] Renooij, S., Probability elicitation for belief networks: issues to consider, Knowl. Eng. Rev., 16, 255-269 (2001)
[27] Roth, D., On the hardness of approximate reasoning, Artif. Intell., 82, 273-302 (1996) · Zbl 1506.68143
[28] Woudenberg, S. P.D.; van der Gaag, L. C., Using the noisy-OR model can be harmful ... but it often is not, (Liu, W., Proceedings of the 11th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (2011), Springer-Verlag: Springer-Verlag Berlin), 122-133 · Zbl 1341.68272
[29] Xiang, Y.; Jia, N., Modeling causal reinforcement and undermining for efficient CPT elicitation, IEEE Trans. Knowl. Data Eng., 19, 1708-1718 (2007)
[30] Xiang, Y., Non-impeding noisy-AND tree causal models over multi-valued variables, Int. J. Approx. Reason., 53, 988-1002 (2012) · Zbl 1264.68185
[31] Zagorecki, A.; Druzdzel, M., An empirical study of probability elicitation under noisy-OR assumption, (Proceedings of the 17th International Florida Artificial Intelligence Research Symposium (2004)), 880-885
[32] Zagorecki, A.; Druzdzel, M. J., Knowledge engineering for Bayesian networks: how common are noisy-MAX distributions in practice?, IEEE Trans. Syst. Man Cybern., 43, 186-195 (2013)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.