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Accuracy vs. Simplicity: A Complex Trade-Off

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  • Enriqueta Aragones

    ()

  • Itzhak Gilboa
  • Andrew Postlewaite
  • David Schmeidler

Abstract

Inductive learning aims at finding general rules that hold true in a database. Targeted learning seeks rules for the predictions of the value of a variable based on the values of others, as in the case of linear or non-parametric regression analysis. Non-targeted learning finds regularities without a specific prediction goal. We model the product of non-targeted learning as rules that state that a certain phenomenon never happens, or that certain conditions necessitate another. For all types of rules, there is a trade-off between the rule's accuracy and its simplicity. Thus rule selection can be viewed as a choice problem, among pairs of degree of accuracy and degree of complexity. However, one cannot in general tell what is the feasible set in the accuracy-complexity space. Formally, we show that finding out whether a point belongs to this set is computationally hard. In particular, in the context of linear regression, finding a small set of variables that obtain a certain value of R2 is computationally hard. Computational complexity may explain why a person is not always aware of rules that, if asked, she would find valid. This, in turn, may explain why one can change other people's minds (opinions, beliefs) without providing new information.

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Paper provided by Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) in its series UFAE and IAE Working Papers with number 564.03.

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Length: 47
Date of creation: 01 2003
Date of revision:
Handle: RePEc:aub:autbar:564.03

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  1. Itzhak Gilboa & David Schmeidler, 2002. "Inductive Inference: An Axiomatic Approach," Levine's Working Paper Archive 391749000000000544, David K. Levine.
  2. Itzhak Gilboa & David Schmeidler, 2001. "Cognitive Foundations of Probability," Cowles Foundation Discussion Papers 1340, Cowles Foundation for Research in Economics, Yale University.
  3. Rafael LaPorta & Florencio Lopez-de-Silanes & Andrei Shleifer & Robert Vishny, . "The Quality of Government," Working Paper 19452, Harvard University OpenScholar.
  4. Kreps, David M, 1979. "A Representation Theorem for "Preference for Flexibility"," Econometrica, Econometric Society, vol. 47(3), pages 565-77, May.
  5. Itzhak Gilboa, 1993. "Hempel, Good and Bayes," Discussion Papers 1045, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Dekel, Eddie & Lipman, Barton L. & Rustichini, Aldo, 1998. "Recent developments in modeling unforeseen contingencies," European Economic Review, Elsevier, vol. 42(3-5), pages 523-542, May.
  7. Gilboa,Itzhak & Schmeidler,David, 2001. "A Theory of Case-Based Decisions," Cambridge Books, Cambridge University Press, number 9780521003117, October.
  8. Bray, Margaret M & Savin, Nathan E, 1986. "Rational Expectations Equilibria, Learning, and Model Specification," Econometrica, Econometric Society, vol. 54(5), pages 1129-60, September.
  9. Eddie Dekel, 1997. "A Unique Subjective State Space for Unforeseen Contingencies," Discussion Papers 1202, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  10. Enriqueta Aragones & Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2013. "Rhetoric and Analogies," UFAE and IAE Working Papers 932.13, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  11. Anderlini, Luca & Felli, Leonardo, 1994. "Incomplete Written Contracts: Undescribable States of Nature," The Quarterly Journal of Economics, MIT Press, vol. 109(4), pages 1085-1124, November.
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Cited by:
  1. Xavier Gabaix & David Laibson & Guillermo Moloche & Stephen Weinberg, 2005. "Information Acquisition: Experimental Analysis of a Boundedly Rational Model," Levine's Bibliography 666156000000000480, UCLA Department of Economics.
  2. Gabaix, Xavier & Laibson, David Isaac & Moloche, Guillermo & Stephen, Weinberg, 2003. "The allocation of attention: theory and evidence," MPRA Paper 47339, University Library of Munich, Germany.

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