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Model selection with the Loss Rank Principle

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  • Hutter, Marcus
  • Tran, Minh-Ngoc

Abstract

A key issue in statistics and machine learning is to automatically select the "right" model complexity, e.g., the number of neighbors to be averaged over in k nearest neighbor () regression or the polynomial degree in regression with polynomials. We suggest a novel principle-the Loss Rank Principle (LoRP)-for model selection in regression and classification. It is based on the loss rank, which counts how many other (fictitious) data would be fitted better. LoRP selects the model that has minimal loss rank. Unlike most penalized maximum likelihood variants (AIC, BIC, MDL), LoRP depends only on the regression functions and the loss function. It works without a stochastic noise model, and is directly applicable to any non-parametric regressor, like .

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:5:p:1288-1306
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    References listed on IDEAS

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    1. Hansheng Wang & Runze Li & Chih-Ling Tsai, 2007. "Tuning parameter selectors for the smoothly clipped absolute deviation method," Biometrika, Biometrika Trust, vol. 94(3), pages 553-568.
    2. Yuhong Yang, 2005. "Can the strengths of AIC and BIC be shared? A conflict between model indentification and regression estimation," Biometrika, Biometrika Trust, vol. 92(4), pages 937-950, December.
    3. 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.
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