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Irrelevant Natural Extension for Choice Functions

Arthur Van Camp (UGent) and Enrique Miranda (UGent)
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Abstract
We consider coherent choice functions under the recent axiomatisation proposed by De Bock and De Cooman that guarantees a representation in terms of binary preferences, and we discuss how to define conditioning in this framework. In a multivariate context, we propose a notion of marginalisation, and its inverse operation called weak (cylindrical) extension. We combine this with our definition of conditioning to define a notion of irrelevance, and we obtain the irrelevant natural extension in this framework: the least informative choice function that satisfies a given irrelevance assessment.
Keywords
Choice functions, coherence, sets of desirable gambles, natural extension, conditioning, epistemic irrelevance

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Citation

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Chicago
Van Camp, Arthur, and Enrique Miranda. 2019. “Irrelevant Natural Extension for Choice Functions.” In , ed. Jasper De Bock, Cassio P. de Campos, Gert De Cooman, Erik Quaeghebeur, and Gregory Wheeler, 103:414–423. Proceedings of Machine Learning Research.
APA
Van Camp, A., & Miranda, E. (2019). Irrelevant Natural Extension for Choice Functions. In Jasper De Bock, C. P. de Campos, G. De Cooman, E. Quaeghebeur, & G. Wheeler (Eds.), (Vol. 103, pp. 414–423). Presented at the the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, Proceedings of Machine Learning Research.
Vancouver
1.
Van Camp A, Miranda E. Irrelevant Natural Extension for Choice Functions. In: De Bock J, de Campos CP, De Cooman G, Quaeghebeur E, Wheeler G, editors. Proceedings of Machine Learning Research; 2019. p. 414–23.
MLA
Van Camp, Arthur, and Enrique Miranda. “Irrelevant Natural Extension for Choice Functions.” Ed. Jasper De Bock et al. Vol. 103. Proceedings of Machine Learning Research, 2019. 414–423. Print.
@inproceedings{8623856,
  abstract     = {We consider coherent choice functions under the recent axiomatisation proposed by De Bock and De Cooman that guarantees a representation in terms of binary preferences, and we discuss how to define conditioning in this framework. In a multivariate context, we propose a notion of marginalisation, and its inverse operation called weak (cylindrical) extension. We combine this with our definition of conditioning to define a notion of irrelevance, and we obtain the irrelevant natural extension in this framework: the least informative choice function that satisfies a given irrelevance assessment.},
  author       = {Van Camp, Arthur and Miranda, Enrique},
  editor       = {De Bock, Jasper and de Campos, Cassio P. and De Cooman, Gert and Quaeghebeur, Erik and Wheeler, Gregory},
  keywords     = {Choice functions,coherence,sets of desirable gambles,natural extension,conditioning,epistemic irrelevance},
  language     = {eng},
  location     = {Thagaste, Ghent, Belgium},
  pages        = {414--423},
  publisher    = {Proceedings of Machine Learning Research},
  title        = {Irrelevant Natural Extension for Choice Functions},
  volume       = {103},
  year         = {2019},
}