Feature Screening via Mutual Information Learning Based on Nonparametric Density Estimation

Abstract

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.

Model-Free Feature Screening via Maximal Information Coefficient (MIC) for Ultrahigh-Dimensional Multiclass Classification

“…In the subsequent sections, we will establish the theoretical properties of the proposed independence screening procedure. Previous studies by Fan and Lv [1], Ji and Jin [22], Zhou and Wang [20] and Ni and Fang [16] have demonstrated that the sure screening property ensures the effectiveness of the independence screening procedure. Hence, it is crucial to establish the sure screening property for MIC-SIS.…”

“…The fundamental principle underlying the maximal information coefficient (MIC) is based on the concept of mutual information. Mutual Information (MI) [20] is a valuable measure in information theory, quantifying the amount of information contained in one random variable regarding another random variable. It represents the reduction in uncertainty of a random variable due to the knowledge of another random variable.…”

“…According to Fan and Lv [1] and Cui [13], condition (C3) allows the minimum true signal to disappear to zero in the order of n τ − as the sample size goes to infinity. According to the sure screening property proposed by Zhou and Wang [20], then condition (C4) is established. Condition (C5) guarantees that the proportion of each class of variables cannot be either extremely small or extremely large.…”