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Optimal categorization

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  • Mohlin, Erik

Abstract

This paper studies categorizations that are optimal for the purpose of making predictions. A subject encounters an object (x,y). She observes the first component, x, and has to predict the second component, y. The space of objects is partitioned into categories. The subject determines what category the new object belongs to on the basis of x, and predicts that its y-value will be equal to the average y-value among the past observations in that category. The optimal categorization minimizes the expected prediction error. The main results are driven by a bias-variance trade-off: The optimal size of a category around x, is increasing in the variance of y conditional on x, decreasing in the variance of the conditional mean, decreasing in the size of the data base, and decreasing in the marginal density over x.

Suggested Citation

  • Mohlin, Erik, 2014. "Optimal categorization," Journal of Economic Theory, Elsevier, vol. 152(C), pages 356-381.
  • Handle: RePEc:eee:jetheo:v:152:y:2014:i:c:p:356-381
    DOI: 10.1016/j.jet.2014.03.007
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    References listed on IDEAS

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    Cited by:

    1. Natalia Shestakova, 2010. "Pricing Scheme Choice: How Process Affects Outcome," CERGE-EI Working Papers wp411, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    2. Topi Miettinen, 2012. "Paying attention to payoffs in analogy-based learning," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(1), pages 193-222, May.
    3. Ennio Bilancini & Leonardo Boncinelli, 2014. "Persuasion with Reference Cues and Elaboration Costs," Center for Economic Research (RECent) 102, University of Modena and Reggio E., Dept. of Economics "Marco Biagi".
    4. Yuval Heller & Eyal Winter, 2016. "Rule Rationality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57, pages 997-1026, August.
    5. Mengel, Friederike & Sciubba, Emanuela, 2014. "Extrapolation and structural similarity in games," Economics Letters, Elsevier, vol. 125(3), pages 381-385.
    6. Chollete, Loran & Schmeidler, David, 2014. "Demand-Theoretic Approach to Choice of Priors," UiS Working Papers in Economics and Finance 2014/14, University of Stavanger.
    7. Bleile, Jörg, 2016. "Categorization based Belief formations," Center for Mathematical Economics Working Papers 519, Center for Mathematical Economics, Bielefeld University.
    8. Vessela Daskalova & Nicolaas J. Vriend, 2014. "Categorization and Coordination," Working Papers 719, Queen Mary University of London, School of Economics and Finance.

    More about this item

    Keywords

    Categorization; Priors; Coarse reasoning; Similarity-based reasoning; Case-based reasoning; Regression trees;

    JEL classification:

    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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