Feature Screening via Mutual Information Learning Based on Nonparametric Density Estimation

With the advent of the era of big data, feature selection in high- or ultra-high-dimensional data is increasingly important in statistics and machine learning fields. In this paper, we propose a marginal utility measure screening method MI-SIS based on mutual information. The proposed marginal utility measure has several appealing features compared with the existing independence screening methods. Firstly, the proposed procedure is model-free without specifying any relationship between the predictors and the response and is valid under a wide range of model settings including parametric and nonparametric models. Secondly, it is suitable for various combinations of the continuous and categorical of predictors and response in our new method. Finally, the new procedure has a good performance in discovering a weak signal in the finite sample and its computation is simple and easy to implement. We establish the sure screening property for the proposed procedure with mild conditions. Simulation experiments and real data applications are presented to illustrate the finite sample performance of the proposed procedures.