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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. 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.
    2. Fischer, Aurélie, 2010. "Quantization and clustering with Bregman divergences," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2207-2221, October.
    3. Mary-Huard, Tristan & Robin, Stéphane & Daudin, Jean-Jacques, 2007. "A penalized criterion for variable selection in classification," Journal of Multivariate Analysis, Elsevier, vol. 98(4), pages 695-705, April.
    4. Eric Mbakop & Max Tabord‐Meehan, 2021. "Model Selection for Treatment Choice: Penalized Welfare Maximization," Econometrica, Econometric Society, vol. 89(2), pages 825-848, March.
    5. Daudin, Jean-Jacques & Mary-Huard, Tristan, 2008. "Estimation of the conditional risk in classification: The swapping method," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3220-3232, February.
    6. Cipollini, Francesca & Oneto, Luca & Coraddu, Andrea & Murphy, Alan John & Anguita, Davide, 2018. "Condition-based maintenance of naval propulsion systems: Data analysis with minimal feedback," Reliability Engineering and System Safety, Elsevier, vol. 177(C), pages 12-23.
    7. 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.
    8. Jiun-Hua Su, 2019. "Model Selection in Utility-Maximizing Binary Prediction," Papers 1903.00716, arXiv.org, revised Jul 2020.
    9. 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.
    10. Adam B. Kashlak & John A. D. Aston & Richard Nickl, 2019. "Inference on Covariance Operators via Concentration Inequalities: k-sample Tests, Classification, and Clustering via Rademacher Complexities," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 214-243, February.
    11. Thomas M. Russell, 2020. "Policy Transforms and Learning Optimal Policies," Papers 2012.11046, arXiv.org.

    More about this item

    Keywords

    Complexity regularization; model selection; error estimation; concentration of measure;
    All these keywords.

    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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