Manifold optimization for nonnegative coefficient logistic regression

摘要

A novel estimation algorithm is introduced for logistic regression model with nonnegative coefficients constraints. The basic idea is to decompose the model parameters as a vector of convex coefficients (the multinomial manifold) and a scaling parameter, which are then optimized alternatively based on the maximum likelihood cost function. The first and second order Riemannian geometry of the multinomial manifold are utilized in the Riemannian trust-region algorithm. The scaling parameter is solved using the golden section algorithm. Numerical examples are employed to demonstrate that effectiveness of the proposed approach.