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Model selection and error estimation

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Abstract

We study model selection strategies based on penalized empirical loss minimization. We point out a tight relationship between error estimation and data-based complexity penalization: any good error estimate may be converted into a data-based penalty function and the performance of the estimate is governed by the quality of the error estimate. We consider several penalty functions, involving error estimates on independent test data, empirical {\sc vc} dimension, empirical {\sc vc} entropy, and margin-based quantities. We also consider the maximal difference between the error on the first half of the training data and the second half, and the expected maximal discrepancy, a closely related capacity estimate that can be calculated by Monte Carlo integration. Maximal discrepancy penalty functions are appealing for pattern classification problems, since their computation is equivalent to empirical risk minimization over the training data with some labels flipped.

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  • Peter L. Bartlett & Stéphane Boucheron & Gábor Lugosi, 2000. "Model selection and error estimation," Economics Working Papers 508, Department of Economics and Business, Universitat Pompeu Fabra.
  • Handle: RePEc:upf:upfgen:508
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    Cited by:

    1. Hutter, Marcus & Tran, Minh-Ngoc, 2010. "Model selection with the Loss Rank Principle," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1288-1306, May.
    2. Alessio Sancetta, 2010. "Bootstrap model selection for possibly dependent and heterogeneous data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(3), pages 515-546, June.
    3. Fischer, Aurélie, 2010. "Quantization and clustering with Bregman divergences," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2207-2221, October.
    4. Olivier Bousquet, 2003. "New approaches to statistical learning theory," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(2), pages 371-389, June.

    More about this item

    Keywords

    Complexity regularization; model selection; error estimation; concentration of measure;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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