Multiclass-penalized logistic regression

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.