Variable selection for sparse logistic regression

We consider the variable selection problem in a sparse logistical regression model. Inspired by the square-root Lasso, we develop a weighted score Lasso for logistical regression. The new method yields the estimation l(1) error bound under similar assumptions as introduced in Bach et al. (Electron J Stat 4:384-414, 2010). Compared to standard Lasso, the weighted score Lasso provides a direct choice for the tuning parameter. Both theoretical and simulation results confirm the satisfactory performance of the proposed method. We illustrate our methodology with a real microarray data set.