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An Efficient Probabilistic Merging Procedure Applied to Statistical Matching

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Book cover Advances in Artificial Intelligence: From Theory to Practice (IEA/AIE 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10351))

Abstract

We propose to use a recently introduced merging procedure for jointly inconsistent probabilistic assessments to the statistical matching problem. The merging procedure is based on an efficient L1 distance minimization through mixed-integer linear programming that results not only feasible but also meaningful for imprecise (lower-upper) probability evaluations elicitation. Significance of the method can be appreciated whenever among quantities (events) there are logical (structural) constraints and there are different sources of information. Statistical matching problem has these features and is characterized by a set of random (discrete) variables that cannot be jointly observed. Separate observations share some common variable and this, together with structural constraints, make sometimes inconsistent the estimates of probability occurrences. Even though estimates on statistical matching are mainly conditional probabilities, inconsistencies appear only on events with the same conditioning, hence the correction procedure can be easily reduced to unconditional cases and the aforementioned procedure applied.

Research partially supported by the INdAM–GNAMPA Project 2016 U2016/000391.

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References

  1. Baioletti, M., Capotorti, A.: Efficient L1-based probability assessments correction: algorithms and applications to belief merging and revision. In: ISIPTA 2015 Proceeding of the 9th International Symposium on Imprecise Probability: Theories and Applications, Pescara (IT), pp. 37–46. ARACNE (2015)

    Google Scholar 

  2. Biazzo, V., Gilio, A.: Some theoretical properties of conditional probability assessments. In: Godo, L. (ed.) ECSQARU 2005. LNCS, vol. 3571, pp. 775–787. Springer, Heidelberg (2005). doi:10.1007/11518655_65

    Chapter  Google Scholar 

  3. Brozzi, A., Capotorti, A., Vantaggi, B.: Incoherence correction strategies in statistical matching. Int. J. Approximate Reasoning 53(8), 1124–1136 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  4. Capotorti, A.: Benefits of embedding structural constraints in coherent diagnostic processes. Int. J. Approximate Reasoning 39(2–3), 211–233 (2005)

    Article  MATH  Google Scholar 

  5. Capotorti, A.: A further empirical study on the over-performance of estimate correction in statistical matching. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds.) IPMU 2012. CCIS, vol. 300, pp. 124–133. Springer, Heidelberg (2012). doi:10.1007/978-3-642-31724-8_14

    Chapter  Google Scholar 

  6. Capotorti, A., Vantaggi, B.: Incoherence correction strategies in statistical matching. In: ISIPTA 2011 Proceeding of the 7th International Symposium on Imprecise Probability: Theories and Applications, Innsbruck, pp. 109–118. SIPTA (2011)

    Google Scholar 

  7. Coletti, G.: Numerical and qualitative judgments in probabilistic expert systems. In: Scozzafava, R. (ed.) Proceeding of the International Workshop on Probabilistic Methods in Expert Systems, pp. 37–55. SIS, Roma (1993)

    Google Scholar 

  8. Coletti, G.: Coherent numerical and ordinal probabilistic assessments. IEEE Trans. Syst. Man Cybern. 24, 1747–1754 (1994)

    Article  MathSciNet  Google Scholar 

  9. Coletti, G., Scozzafava, R.: Probabilistic Logic in a Coherent Setting. Trends in Logic. Kluwer, Dordrecht (2002)

    Book  MATH  Google Scholar 

  10. Cozman, F.G., Ianni, L.F.: Probabilistic satisfiability and coherence checking through integer programming. In: Gaag, L.C. (ed.) ECSQARU 2013. LNCS, vol. 7958, pp. 145–156. Springer, Heidelberg (2013). doi:10.1007/978-3-642-39091-3_13

    Chapter  Google Scholar 

  11. De Bona, G., Finger, M.: Measuring inconsistency in probabilistic logic: rationality postulates and Dutch book interpretation. Artif. Intell. 227, 140–164 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  12. D’Orazio, M., Di Zio, M., Scanu, M.: Statistical Matching: Theory and Practice. Wiley, New York (2006)

    Book  MATH  Google Scholar 

  13. D’Orazio, M., Di Zio, M., Scanu, M.: Statistical matching for categorical data: displaying uncertainty and using logical constraints. J. Off. Stat. 22, 137–157 (2006)

    Google Scholar 

  14. Di Zio, M., Vantaggi, B.: Partial identification in statistical matching with misclassification. Int. J. Approximate Reasoning 82, 227–241 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  15. Gilio, A.: Probabilistic consistency of knowledge bases in inference systems. In: Clarke, M., Kruse, R., Moral, S. (eds.) ECSQARU 1993. LNCS, vol. 747, pp. 160–167. Springer, Heidelberg (1993). doi:10.1007/BFb0028196

    Chapter  Google Scholar 

  16. Gilio, A., Pfeifer, N., Sanfilippo, G.: Transitivity in coherence-based probability logic. J. Appl. Logic 14, 46–64 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  17. Vantaggi, B.: Statistical matching of multiple sources: a look through coherence. Int. J. Approximate Reasoning 49(3), 701–711 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  18. Walley, P.: Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, London (1991)

    Book  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Perugia, Italy

    Marco Baioletti & Andrea Capotorti

Authors
  1. Marco Baioletti
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  2. Andrea Capotorti
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Correspondence to Andrea Capotorti .

Editor information

Editors and Affiliations

  1. Artois University, Lens, France

    Salem Benferhat

  2. Artois University, Lens, France

    Karim Tabia

  3. Texas State University, San Marcos, Texas, USA

    Moonis Ali

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Baioletti, M., Capotorti, A. (2017). An Efficient Probabilistic Merging Procedure Applied to Statistical Matching. In: Benferhat, S., Tabia, K., Ali, M. (eds) Advances in Artificial Intelligence: From Theory to Practice. IEA/AIE 2017. Lecture Notes in Computer Science(), vol 10351. Springer, Cham. https://doi.org/10.1007/978-3-319-60045-1_9

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  • DOI: https://doi.org/10.1007/978-3-319-60045-1_9

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  • Online ISBN: 978-3-319-60045-1

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