Functional data regression model based on functional mean variance estimation and mutual information weighted ensemble learning

Abstract

Functional data regression model holds significant application value in various fields such as medicine, economics, finance, and industrial manufacturing.    This paper introduces a novel functional regression method that incorporates functional mean variance estimation and mutual information weighted ensemble learning. The proposed method employs functional mean variance estimation to reduce dimension while maintaining the effective information of the predictor related to the response variable. Specifically, this method projects the random function into the function space spanned by finite dimensional basis functions to extract the underlying functional information of the original data. Additionally, considering that the number of sufficient dimension reduction sub-directions is unknown, this paper proposes a model averaging approach based on mutual information weighting to determine the importance of each sub-model. The proposed method can adaptively address the over-fitting and under-fitting problems of the prediction model. The empirical data analysis indicates that the proposed method outperforms other comparison methods in terms of smaller mean square error and absolute error, and it exhibits a certain level of robustness.