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Maximum Likelihood Estimation and Coarse Data

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Scalable Uncertainty Management (SUM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10564))

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Abstract

The term coarse data encompasses different types of incomplete data where the (partial) information about the outcomes of a random experiment can be expressed in terms of subsets of the sample space. We consider situations where the coarsening process is stochastic, and illustrate with examples how ignoring this process may produce misleading estimations.

The first author thanks the Program Committee Chairs for their kind invitation to participate in the conference. The research in this work has been supported by TIN2014-56967-R (Spanish Ministry of Science and Innovation) and FC-15-GRUPIN14-073 (Regional Ministry of the Principality of Asturias).

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Notes

  1. 1.

    Let the reader notice that this vector does not necessarily represent a probability distribution. In fact, the sum \(\sum _{j=1}^r q_j\) is strictly greater than 1, unless the collection of \(A_j\) forms a partition of \(\mathcal {X}\).

References

  1. Ahmadi, M., Hüllermeier, E., Couso I.:, Statistical inference for incomplete ranking data: the case of rank-dependent coarsening. In: Proceedings of the 34th International Conference on Machine Learning (2017 ICML), Sydney (Australia)

    Google Scholar 

  2. Chib, S.: Marginal likelihood from the Gibbs output. J. Am. Stat. Assoc. 90, 1313–1321 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  3. Couso, I., Ahmadi, M., Hüllermeier, E.: Statistical inference for incomplete ranking data: a comparison of two likelihood-based estimators. In: Proceedings of DA2PL 2016 (From Multiple Criteria Decision Aid to Preference Learning), Paderborn (Germany) (2016)

    Google Scholar 

  4. Couso, I., Dubois, D.: Statistical reasoning with set-valued information: ontic vs. epistemic views. Int. J. Approximate Reasoning 55, 1502–1518 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  5. Couso, I., Dubois, D.: Belief revision and the EM algorithm. In: Carvalho, J.P., Lesot, M.-J., Kaymak, U., Vieira, S., Bouchon-Meunier, B., Yager, R.R. (eds.) IPMU 2016. CCIS, vol. 611, pp. 279–290. Springer, Cham (2016). doi:10.1007/978-3-319-40581-0_23

    Google Scholar 

  6. Couso, I., Dubois, D.: Maximum likelihood under incomplete information: toward a comparison of criteria. In: Ferraro, M.B., Giordani, P., Vantaggi, B., Gagolewski, M., Gil, M.Á., Grzegorzewski, P., Hryniewicz, O. (eds.) Soft Methods for Data Science. AISC, vol. 456, pp. 141–148. Springer, Cham (2017). doi:10.1007/978-3-319-42972-4_18

    Chapter  Google Scholar 

  7. Couso, I., Dubois, D.: A general framework for maximizing likelihood under incomplete data, under review

    Google Scholar 

  8. Couso, I., Dubois, D., Sánchez, L.: Random Sets and Random Fuzzy Sets as Ill-Perceived Random Variables. SAST. Springer, Cham (2014). doi:10.1007/978-3-319-08611-8

    Book  MATH  Google Scholar 

  9. Dawid, A.P., Dickey, J.M.: Likelihood and Bayesian inference from selectively reported data. J. Amer. Statist. Assoc. 72, 845–850 (1977)

    MathSciNet  MATH  Google Scholar 

  10. Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm (with discussion). J. Roy. Statist. Soc. B 39, 1–38 (1977)

    MathSciNet  MATH  Google Scholar 

  11. Denœux, T.: Maximum likelihood estimation from uncertain data in the belief function framework. IEEE Trans. Knowl. Data Eng. 26, 119–130 (2013)

    Article  Google Scholar 

  12. Edwards, A.W.F.: Likelihood. Cambridge University Press, Cambridge (1972)

    MATH  Google Scholar 

  13. Guillaume, R., Dubois, D.: Robust parameter estimation of density functions under fuzzy interval observations. In: 9th ISIPTA Symposium, Pescara, Italy, pp. 147–156 (2015)

    Google Scholar 

  14. Guillaume, R., Couso, I., Dubois, D.: Maximum likelihood and robust optimisation on coarse data. In: 10th ISIPTA Symposium, Lugano, Switzerland, pp. 147–156 (2017)

    Google Scholar 

  15. Heitjan, D.F., Rubin, D.B.: Ignorability and coarse data. Ann. Stat. 19, 2244–2253 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  16. Huber, P.J.: The behavior of maximum likelihood estimates under nonstandard conditions. In: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 221–233. University of California Press (1967)

    Google Scholar 

  17. Hüllermeier, E.: Learning from imprecise and fuzzy observations: data disambiguation through generalized loss minimization. Int. J. Approximate Reasoning 55, 1519–1534 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  18. Hüllermeier, E., Cheng, W.: Superset learning based on generalized loss minimization. In: Appice, A., Rodrigues, P.P., Santos Costa, V., Gama, J., Jorge, A., Soares, C. (eds.) ECML PKDD 2015. LNCS, vol. 9285, pp. 260–275. Springer, Cham (2015). doi:10.1007/978-3-319-23525-7_16

    Chapter  Google Scholar 

  19. Jaeger, M.: Ignorability in statistical and probabilistic inference. J. Artif. Intell. Res. (JAIR) 24, 889–917 (2005)

    MathSciNet  MATH  Google Scholar 

  20. Jaeger, M.: The AI&M procedure for learning from incomplete data. In: Proceedings of Uncertainty in Artificial Intelligence Conference (UAI-06), pp. 225–232 (2006)

    Google Scholar 

  21. Plass, J., Augustin, T., Cattaneo, M., Schollmeyer, G.: Statistical modelling under epistemic data imprecision: some results on estimating multinomial distributions and logistic regression for coarse categorical data. In: Proceedings of the 9th International Symposium on Imprecise Probability: Theories and Applications (ISIPTA 2015), Pescara (Italy) (2015)

    Google Scholar 

  22. Plass, J., Cattaneo, M.E.G.V., Schollmeyer, G., Augustin, T.: Testing of coarsening mechanisms: coarsening at random versus subgroup independence. In: Ferraro, M.B., Giordani, P., Vantaggi, B., Gagolewski, M., Gil, M.Á., Grzegorzewski, P., Hryniewicz, O. (eds.) Soft Methods for Data Science. AISC, vol. 456, pp. 415–422. Springer, Cham (2017). doi:10.1007/978-3-319-42972-4_51

    Chapter  Google Scholar 

  23. Quost, B., Denœux, T.: Clustering and classification of fuzzy data using the fuzzy EM algorithm. Fuzzy Sets Syst. 286, 134–156 (2016)

    Article  MathSciNet  Google Scholar 

  24. Ramasso, E., Denœux, T.: Making use of partial knowledge about hidden states in HMMs: an approach based on belief functions. IEEE Trans. Fuzzy Syst. 22(2), 395–405 (2014)

    Article  Google Scholar 

  25. Sid-Sueiro, J.: Proper losses for learning from partial labels. In: Proceedings of Neural Information Processing Systems Conference (NIPS 2012), Lake Tahoe, Nevada, USA (2012)

    Google Scholar 

  26. Smets, P.: Constructing the pignistic probability function in a context of uncertainty. In: Henrion M., et al. (eds.) Uncertainty in Artificial Intelligence 5, pp. 29–39. North-Holland, Amsterdam (1990)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Statistics and O.R., Universidad de Oviedo, Oviedo, Spain

    Inés Couso

  2. IRIT, CNRS Université Paul Sabatier, Toulouse, France

    Didier Dubois

  3. Department of Computer Science, Universität Paderborn, Paderborn, Germany

    Eyke Hüllermeier

Authors
  1. Inés Couso
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  2. Didier Dubois
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  3. Eyke Hüllermeier
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Corresponding author

Correspondence to Inés Couso .

Editor information

Editors and Affiliations

  1. University of Granada, Granada, Spain

    Serafín Moral

  2. University of Rennes I, Lannion, France

    Olivier Pivert

  3. University of Granada, Granada, Spain

    Daniel Sánchez

  4. University of Granada, Granada, Spain

    Nicolás Marín

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Couso, I., Dubois, D., Hüllermeier, E. (2017). Maximum Likelihood Estimation and Coarse Data. In: Moral, S., Pivert, O., Sánchez, D., Marín, N. (eds) Scalable Uncertainty Management. SUM 2017. Lecture Notes in Computer Science(), vol 10564. Springer, Cham. https://doi.org/10.1007/978-3-319-67582-4_1

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  • DOI: https://doi.org/10.1007/978-3-319-67582-4_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67581-7

  • Online ISBN: 978-3-319-67582-4

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