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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.
    2. Vincent, Martin & Hansen, Niels Richard, 2014. "Sparse group lasso and high dimensional multinomial classification," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 771-786.
    3. Cramer, J. S. & Ridder, G., 1991. "Pooling states in the multinomial logit model," Journal of Econometrics, Elsevier, vol. 47(2-3), pages 267-272, February.
    4. 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).
    5. Elaine Zanutto & Eric Bradlow, 2006. "Data pruning in consumer choice models," Quantitative Marketing and Economics (QME), Springer, vol. 4(3), pages 267-287, September.
    6. Carson, Richard T. & Louviere, Jordan J., 2014. "Statistical properties of consideration sets," Journal of choice modelling, Elsevier, vol. 13(C), pages 37-48.
    7. Didier Nibbering, 2019. "A High-dimensional Multinomial Choice Model," Monash Econometrics and Business Statistics Working Papers 19/19, Monash University, Department of Econometrics and Business Statistics.
    8. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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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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