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Multiclass-penalized logistic regression

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  • Nibbering, Didier
  • Hastie, Trevor J.

Abstract

A multinomial logistic regression model that penalizes the number of class-specific parameters is proposed. The number of parameters in a standard multinomial regression model increases linearly with the number of classes and number of explanatory variables. The multiclass-penalized regression model clusters parameters together by penalizing the differences between class-specific parameter vectors, instead of penalizing the number of explanatory variables. The model provides interpretable parameter estimates, even in settings with many classes. An algorithm for maximum likelihood estimation in the multiclass-penalized regression model is discussed. Applications to simulated and real data show in- and out-of-sample improvements in performance relative to a standard multinomial regression model.

Suggested Citation

  • Nibbering, Didier & Hastie, Trevor J., 2022. "Multiclass-penalized logistic regression," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:csdana:v:169:y:2022:i:c:s0167947321002486
    DOI: 10.1016/j.csda.2021.107414
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    References listed on IDEAS

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    1. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
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    5. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
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    Cited by:

    1. Aaron J. Molstad & Keshav Motwani, 2023. "Multiresolution categorical regression for interpretable cell‐type annotation," Biometrics, The International Biometric Society, vol. 79(4), pages 3485-3496, December.

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