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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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 152 (2014)
Issue (Month): C ()
Pages: 356-381

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Handle: RePEc:eee:jetheo:v:152:y:2014:i:c:p:356-381

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Web page: http://www.elsevier.com/locate/inca/622869

Related research

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

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References

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  1. Philippe Jeniel, 2001. "Analogy-Based Expectation Equilibrium," Economics Working Papers 0003, Institute for Advanced Study, School of Social Science.
  2. Philippe Jehiel & Frédéric Koessler, 2006. "Revisiting Games of Incomplete Information with Analogy-Based Expectations," Levine's Bibliography 122247000000000252, UCLA Department of Economics.
  3. Philippe Jehiel & Dov Samet, 2003. "Valuation Equilibria," Game Theory and Information 0310003, EconWPA.
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  8. Itzhak Gilboa & David Schmeidler, 2001. "Inductive Inference: An Axiomatic Approach," Cowles Foundation Discussion Papers 1339, Cowles Foundation for Research in Economics, Yale University.
  9. Mengel, Friederike, 2012. "Learning across games," Games and Economic Behavior, Elsevier, vol. 74(2), pages 601-619.
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Citations

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Cited by:
  1. Miettinen, Topi, 2009. "Paying Attention to Payoffs in Analogy-Based Learning," SITE Working Paper Series 7, Stockholm Institute of Transition Economics, Stockholm School of Economics.
  2. 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.
  3. Vessela Daskalova & Nicolaas J. Vriend, 2014. "Categorization and Coordination," Working Papers 719, Queen Mary, University of London, School of Economics and Finance.
  4. Natalia Shestakova, 2010. "Pricing Scheme Choice: How Process Affects Outcome," CERGE-EI Working Papers wp411, The Center for Economic Research and Graduate Education - Economic Institute, Prague.
  5. Heller, Yuval & Winter, Eyal, 2013. "Rule Rationality," MPRA Paper 48746, University Library of Munich, Germany.

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