Analysis of symmetry properties for bayesian confirmation measures

Authors:
Salvatore Greco;Roman Słowiński;Izabela Szczęch
Affiliations:
Department of Economics and Business, University of Catania, Italy;Institute of Computing Science, Poznan University of Technology, Poland,Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland;Institute of Computing Science, Poznan University of Technology, Poland
Venue:
RSKT'12 Proceedings of the 7th international conference on Rough Sets and Knowledge Technology
Year:
2012

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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.