An efficient algorithm for the non-convex penalized multinomial logistic regression

Abstract

In this paper, we introduce an efficient algorithm for the non-convex penalized multinomial logistic regression that can be uniformly applied to a class of non-convex penalties. The class includes most non-convex penalties such as the smoothly clipped absolute deviation, minimax concave and bridge penalties. The algorithm is developed based on the concave-convex procedure and modified local quadratic approximation algorithm. However, usual quadratic approximation may slow down computational speed since the dimension of the Hessian matrix depends on the number of categories of the output variable. For this issue, we use a uniform bound of the Hessian matrix in the quadratic approximation. The algorithm is available from the R package ncpen developed by the authors. Numerical studies via simulations and real data sets are provided for illustration.