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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.

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Decision fusion is an effective way to resolve the conflict of diagnosis results. Aiming at the problem that Dempster-Shafer (DS) theory deals with the high conflict of evidence and produces wrong results, a decision fusion algorithm for fault diagnosis based on closeness and DS theory is proposed. Firstly, the relevant concepts of DS theory are introduced, and the normal distribution membership function is used as the evidence closeness. Secondly, the harmonic average is introduced, and the weight of each evidence is established according to the product of closeness of each evidence and its harmonic average. Thirdly, the weight of conflicting evidence is regularized, and the final decision fusion result is obtained by using the Dempster’s rule. Lastly, the simulation and application examples are designed. Simulation and application results show that the method can effectively reduce the impact of diagnostic information conflicts and improve the accuracy of decision fusion. What’s more, the method considers the overall average distribution of evidence in the identification framework, it can reduce evidence conflicts while preserving important diagnostic information.