Abstract
The paper considers symmetry properties of Bayesian confirmation measures, which constitute an important group of interestingness measures for evaluation of rules induced from data. We demonstrate that the symmetry properties proposed in the literature do not fully reflect the concept of confirmation. We conduct a thorough analysis of the symmetries regarding that the confirmation should express how much more probable the rule’s hypothesis is when the premise is present rather than when the premise is absent. As a result we point out which symmetries are desired for Bayesian confirmation measures and which are truly unattractive. Such knowledge is a valuable tools for assessing the quality and usefulness of measures.
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References
Brzezinska, I., Greco, S., Slowinski, R.: Mining Pareto-optimal rules with respect to support and anti-support. Engineering Applications of Artificial Intelligence 20(5), 587–600 (2007)
Carnap, R.: Logical Foundations of Probability, 2nd edn. University of Chicago Press, Chicago (1962)
Crupi, V., Tentori, K., Gonzalez, M.: On Bayesian measures of evidential support: Theoretical and empirical issues. Philosophy of Science 74, 229–252 (2007)
Eells, E., Fitelson, B.: Symmetries and asymmetries in evidential support. Philosophical Studies 107(2), 129–142 (2002)
Fitelson, B.: The Plurality of Bayesian Measures of Confirmation and the Problem of Measure Sensitivity. Philosophy of Science 66, 362–378 (1999)
Fitelson, B.: Studies in Bayesian Confirmation Theory. Ph.D. Thesis, University of Wisconsin, Madison (2001)
Geng, L., Hamilton, H.J.: Interestingness Measures for Data Mining: A Survey. ACM Computing Surveys 38(3), article 9 (2006)
Greco, S., Pawlak, Z., Slowinski, R.: Can Bayesian confirmation measures be useful for rough set decision rules? Engineering Applications of Artificial Intelligence 17, 345–361 (2004)
Hilderman, R., Hamilton, H.: Knowledge Discovery and Measures of Interest. Kluwer Academic Publishers (2001)
Maher, P.: Confirmation Theory. The Encyclopedia of Philosophy, 2nd edn. Macmillan Reference, USA (2005)
McGarry, K.: A survey of interestingness measures for knowledge discovery. The Knowledge Engineering Review 20(1), 39–61 (2005)
Słowiński, R., Brzezinska, I., Greco, S.: Application of Bayesian Confirmation Measures for Mining Rules from Support-Confidence Pareto-Optimal Set (Invited Paper in). In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds.) ICAISC 2006. LNCS (LNAI), vol. 4029, pp. 1018–1026. Springer, Heidelberg (2006)
Słowiński, R., Szczęch, I., Urbanowicz, M., Greco, S.: Mining Association Rules with Respect to Support and Anti-support-Experimental Results. In: Kryszkiewicz, M., Peters, J.F., Rybiński, H., Skowron, A. (eds.) RSEISP 2007. LNCS (LNAI), vol. 4585, pp. 534–542. Springer, Heidelberg (2007)
Szczęch, I.: Multicriteria Attractiveness Evaluation of Decision and Association Rules. In: Peters, J.F., Skowron, A., Wolski, M., Chakraborty, M.K., Wu, W.-Z. (eds.) Transactions on Rough Sets X. LNCS, vol. 5656, pp. 197–274. Springer, Heidelberg (2009)
Szczech, I., Greco, S., Slowinski, R.: New property for rule interestingness measures. In: Ganzha, M., Maciaszek, L., Paprzycki, M. (eds.) Proceedings of the Federated Conference on Computer Science and Information Systems FedCSIS, pp. 103–108 (2011)
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Greco, S., Słowiński, R., Szczęch, I. (2012). Analysis of Symmetry Properties for Bayesian Confirmation Measures. In: Li, T., et al. Rough Sets and Knowledge Technology. RSKT 2012. Lecture Notes in Computer Science(), vol 7414. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31900-6_27
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DOI: https://doi.org/10.1007/978-3-642-31900-6_27
Publisher Name: Springer, Berlin, Heidelberg
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