Multiclass Classification by Sparse Multinomial Logistic Regression

In this paper we consider high-dimensional multiclass classification by sparse multinomial logistic regression. We propose first a feature selection procedure based on penalized maximum likelihood with complexity penalty the model size and derive nonasymptotic bounds for misclassification excess risk of resulting classifier. establish also their tightness deriving corresponding minimax lower bounds. particular, show that there is phase transition between small large number classes. The can be reduced under additional low noise condition. To find solution requires, however, combinatorial search over all possible models. design computationally feasible data, group Lasso Slope classifiers they achieve order.