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Closure operators: Complexity and applications to classification and decision-making

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  • Hamed Hamze Bajgiran
  • Federico Echenique

Abstract

We study the complexity of closure operators, with applications to machine learning and decision theory. In machine learning, closure operators emerge naturally in data classification and clustering. In decision theory, they can model equivalence of choice menus, and therefore situations with a preference for flexibility. Our contribution is to formulate a notion of complexity of closure operators, which translate into the complexity of a classifier in ML, or of a utility function in decision theory.

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  • Hamed Hamze Bajgiran & Federico Echenique, 2022. "Closure operators: Complexity and applications to classification and decision-making," Papers 2202.05339, arXiv.org, revised May 2022.
    • Handle: RePEc:arx:papers:2202.05339
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    References listed on IDEAS

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    1. Eddie Dekel & Barton L Lipman & Aldo Rustichini & Todd Sarver, 2007. "Representing Preferences with a Unique Subjective State Space: A Corrigendum -super-1," Econometrica, Econometric Society, vol. 75(2), pages 591-600, March.
    2. Kreps, David M, 1979. "A Representation Theorem for "Preference for Flexibility"," Econometrica, Econometric Society, vol. 47(3), pages 565-577, May.
    3. Chambers, Christopher P. & Miller, Alan D. & Yenmez, M. Bumin, 2020. "Closure and preferences," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 161-166.
    4. Faruk Gul & Wolfgang Pesendorfer, 2001. "Temptation and Self-Control," Econometrica, Econometric Society, vol. 69(6), pages 1403-1435, November.
    5. Michael Richter & Ariel Rubinstein, 2015. "Back to Fundamentals: Equilibrium in Abstract Economies," American Economic Review, American Economic Association, vol. 105(8), pages 2570-2594, August.
    6. Kopylov, Igor, 2009. "Finite additive utility representations for preferences over menus," Journal of Economic Theory, Elsevier, vol. 144(1), pages 354-374, January.
    7. Chateauneuf, Alain & Jaffray, Jean-Yves, 1989. "Some characterizations of lower probabilities and other monotone capacities through the use of Mobius inversion," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 263-283, June.
    8. Koshevoy, Gleb A., 1999. "Choice functions and abstract convex geometries," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 35-44, July.
    9. Dekel, Eddie & Lipman, Barton L & Rustichini, Aldo, 2001. "Representing Preferences with a Unique Subjective State Space," Econometrica, Econometric Society, vol. 69(4), pages 891-934, July.
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