A Safe Screening Rule for Sparse Logistic Regression
The 1 -regularized logistic regression (or sparse logistic regression) is a widely used method for simultaneous classification and feature selection. Although many recent efforts have been devoted to its efficient implementation, its application to high dimensional data still poses significant challenges. In this paper, we present a fast and effective sparse logistic regression screening rule (Slores) to identify the "0" components in the solution vector, which may lead to a substantial reduction in the number of features to be entered to the optimization. An appealing feature of Slores is that the data set needs to be scanned only once to run the screening and its computational cost is negligible compared to that of solving the sparse logistic regression problem. Moreover, Slores is independent of solvers for sparse logistic regression, thus Slores can be integrated with any existing solver to improve the efficiency. We have evaluated Slores using high-dimensional data sets from different applications. Experiments demonstrate that Slores outperforms the existing state-of-the-art screening rules and the efficiency of solving sparse logistic regression can be improved by one magnitude.
In this paper, the authors propose a new sparse logistic regression screening rule (Slores) for feature selection, which discard the features with zero coefficients by solving a convex optimization problem with closed form solution.  A series of evaluations have been conducted to show its effectiveness.This idea is simple but interesting and I like it. However, I still have some questions:1.	In the section 3, the authors propose to estimate the upper bound by solving a optimization problem, where the critical parameter $\lambda_0$ and $\theta_{\lambda_0}^\ast$ are set to be $\lambda_\max$ and $\theta_{\lambda_{max}}^\ast$ respectively. However, how can we know $\lambda_\max$ and $\theta_{\lambda_{max}}^\ast$ at the beginning?2.	In the 138th row, a “|” is missing in the equation.3.	In the experimental results, the authors just use the reject ratio to measure the performance. However, I still have a problem: whether the non-zero coefficients can be affected by discarding these features? Some other feature selection measures are recommended. 4.	The authors should compare the proposed method with the state-of-the-art, such as “ Lasso Screening Rules via Dual Polytope Projection, ICML, 2013”.