Skip to main content
SpringerLink
Log in

Monotonicity and Symmetry of IFPD Bayesian Confirmation Measures

  • Conference paper
  • First Online:
Book cover Modeling Decisions for Artificial Intelligence (MDAI 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9880))

Abstract

IFPD confirmation measures are used in ranking inductive rules in Data Mining. Many measures of this kind have been defined in literature. We show how some of them are related to each other via weighted means. The special structure of IFPD measures allows to define also new monotonicity and symmetry properties which appear quite natural in such context. We also suggest a way to measure the degree of symmetry of IFPD confirmation measures.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    As a matter of fact, when the evidence E disconfirms conclusion H, i.e. \(P(H|E)<P(H)\), both \(Z_1\) and \(Z_2\) assume a negative value: strictly speaking their harmonic mean is not defined, but the proposed link (1) among measures holds, with the same meaning. In the neutrality case we have the boundary values \(K=Z=0\) and their link cannot be defined by a harmonic mean like (1).

References

  1. Atkinson, D.: Confirmation and justification. A commentary on Shogenji’s measure. Synthese 184, 49–61 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  2. Błaszczyński, J., Greco, S., Matarazzo, B., Słowiński, R.: jMAF - dominance-based rough set data analysis framework. In: Skowron, A., Suraj, Z. (eds.) Rough Sets and Intelligent Systems - Professor Zdzisław Pawlak in Memoriam. ISRL, vol. 42, pp. 185–209. Springer, Heidelberg (2013)

    Google Scholar 

  3. Carnap, R.: Logical Foundations of Probability, 2nd edn. University of Chicago Press, Chicago (1962)

    MATH  Google Scholar 

  4. Crupi, V., Festa, R., Buttasi, C.: Towards a grammar of Bayesian confirmation. In: Suárez, M., Dorato, M., Rédei, M. (eds.) Epistemology and Methodology of Science, pp. 73–93. Springer, Dordrecht (2010)

    Google Scholar 

  5. Eells, E., Fitelson, B.: Symmetries and asymmetries in evidentual support. Philos. Stud. 107, 129–142 (2002)

    Article  Google Scholar 

  6. Fitelson, B.: The plurality of Bayesian measures of confirmation and the problem of measure sensitivity. Philos. Sci. 66, 362–378 (1999)

    Article  MathSciNet  Google Scholar 

  7. Fitelson, B.: Likelihoodism, Bayesianism, and relational confirmation. Synthese 156, 473–489 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  8. Geng, L., Hamilton, H.J.: Interestingness measures for data mining: a survey. ACM Comput. Surv. 38, 1–32 (2006)

    Article  Google Scholar 

  9. Glass, D.H.: Entailment and symmetry in confirmation measures of interestingness. Inf. Sci. 279, 552–559 (2014)

    Article  MathSciNet  Google Scholar 

  10. Good, I.J.: Probability and the Weighing of Evidence. Charles Griffin, London (1950)

    MATH  Google Scholar 

  11. Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press, Cambridge (2009)

    Book  MATH  Google Scholar 

  12. Greco, S., Pawlak, Z., Słowiński, R.: Can Bayesian confirmation measures be useful for rough set decision rules? Eng. Appl. Artif. Intell. 17, 345–361 (2004)

    Article  Google Scholar 

  13. Greco, S., Słowiński, R., Szczȩch, I.: Properties of rule interestingness measures and alternative approaches to normalization of measures. Inf. Sci. 216, 1–16 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  14. Kemeny, J., Oppenheim, P.: Degrees of factual support. Philos. Sci. 19, 307–324 (1952)

    Article  Google Scholar 

  15. Laboratory of Intelligent Decision Support Systems of the Poznan University of Technology. http://idss.cs.put.poznan.pl/site/software.html

  16. Piatetsky-Shapiro, G.: Discovery, Analysis, and Presentation of Strong Rules, pp. 229–248. AAAI/MIT Press, Cambridge (1991)

    Google Scholar 

  17. Rescher, N.: A theory of evidence. Philos. Sci. 25, 83–94 (1958)

    Article  Google Scholar 

  18. Shogenji, T.: The degree of epistemic justification and the conjunction fallacy. Synthese 184, 29–48 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  19. Siburg, K.F., Stoimenov, P.A.: Symmetry of functions and exchangeability of random variables. Stat. Pap. 52, 1–15 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  20. Susmaga, R., Szczech, I.: The property of \(\chi ^2_{01}\)-concordance for Bayesian confirmation measures. In: Torra, V., Narukawa, Y., Navarro-Arribas, G., Megías, D. (eds.) MDAI 2013. LNCS, vol. 8234, pp. 226–236. Springer, Heidelberg (2013)

    Google Scholar 

  21. Susmaga, R., Szczȩch, I.: Can interestingness measures be usefully visualized? Int. J. Appl. Math. Comput. Sci. 25, 323–336 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  22. Wu, X., Zhang, C., Zhang, S.: Efficient mining of both positive and negative association rules. ACM Trans. Inf. Syst. 22, 381–405 (2004)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Management, Ca’ Foscari University of Venice, Fondamenta San Giobbe, Cannaregio 873, 30121, Venezia, Italy

    Emilio Celotto & Andrea Ellero

  2. Department of Economics, Ca’ Foscari University of Venice, Fondamenta San Giobbe, Cannaregio 873, 30121, Venezia, Italy

    Paola Ferretti

Authors
  1. Emilio Celotto
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrea Ellero
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Paola Ferretti
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Paola Ferretti .

Editor information

Editors and Affiliations

  1. University of Kövde , Skövde, Sweden

    Vicenç Torra

  2. Toho Gakuen , Kunitachi, Tokyo, Japan

    Yasuo Narukawa

  3. Enginyeria de la Informacio I de les Com, Univ Autonoma de Barcelona, Bellaterra, Spain

    Guillermo Navarro-Arribas

  4. Universitat d'Andorra , Sant Julià de Lòria, Andorra

    Cristina Yañez

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Celotto, E., Ellero, A., Ferretti, P. (2016). Monotonicity and Symmetry of IFPD Bayesian Confirmation Measures. In: Torra, V., Narukawa, Y., Navarro-Arribas, G., Yañez, C. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2016. Lecture Notes in Computer Science(), vol 9880. Springer, Cham. https://doi.org/10.1007/978-3-319-45656-0_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-45656-0_10

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45655-3

  • Online ISBN: 978-3-319-45656-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation