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Accuracy vs. Simplicity: A Complex Trade-Off

  • E. Aragones
  • I. Gilboa
  • A. Postlewaite
  • D. Schmeidler

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 David K. Levine in its series Levine's Working Paper Archive with number 506439000000000185.

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Date of creation: 24 Jan 2003
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Handle: RePEc:cla:levarc:506439000000000185
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  1. Enriqueta Aragonès & Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2013. "Rhetoric and Analogies," Working Papers 706, Barcelona Graduate School of Economics.
  2. Gilboa, I. & Schmeidler, D., 2001. "Inductive Inference: An Axiomatic Approach," Papers 2001-19, Tel Aviv.
  3. Anderlini, L. & Felli, L., 1993. "Incomplete Written Contracts: Undescribable States of Nature," Papers 183, Cambridge - Risk, Information & Quantity Signals.
  4. 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.
  5. 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.
  6. Bray, Margaret M & Savin, Nathan E, 1986. "Rational Expectations Equilibria, Learning, and Model Specification," Econometrica, Econometric Society, vol. 54(5), pages 1129-60, September.
  7. 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.
  8. Kreps, David M, 1979. "A Representation Theorem for "Preference for Flexibility"," Econometrica, Econometric Society, vol. 47(3), pages 565-77, May.
  9. Itzhak Gilboa & David Schmeidler, 2001. "Cognitive Foundations of Probability," Cowles Foundation Discussion Papers 1340, Cowles Foundation for Research in Economics, Yale University.
  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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