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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. Gilboa, I. & Schmeidler, D., 1999. "Cognitive Foundations of Probability," Papers 30-99, Tel Aviv.
  2. 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).
  3. Rafael La Porta & Florencio Lopez-de-Silanes & Andrei Shleifer & Robert Vishny, 1998. "The Quality of Goverment," NBER Working Papers 6727, National Bureau of Economic Research, Inc.
  4. 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.
  5. 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.
  6. Gilboa, I. & Schmeidler, D., 1999. "Inductive Inference: an Axiomatic Approach," Papers 29-99, Tel Aviv.
  7. Kreps, David M, 1979. "A Representation Theorem for "Preference for Flexibility"," Econometrica, Econometric Society, vol. 47(3), pages 565-77, May.
  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. Anderlini, L. & Felli, L., 1993. "Incomplete Written Contracts: Undescribable States of Nature," Papers 183, Cambridge - Risk, Information & Quantity Signals.
  10. Gilboa,Itzhak & Schmeidler,David, 2001. "A Theory of Case-Based Decisions," Cambridge Books, Cambridge University Press, number 9780521802345.
  11. Itzhak Gilboa, 1993. "Hempel, Good and Bayes," Discussion Papers 1045, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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Cited by:
  1. 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.
  2. 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.

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