Genetic Programming-Based Simultaneous Feature Selection and Imputation for Symbolic Regression with Incomplete Data

Abstract

Symbolic regression via genetic programming has been used successfully for empirical modeling from given data sets. However, real-world data sets might contain missing values. Although there are different approaches to dealing with incomplete data sets for classification, symbolic regression with missing values has been rarely investigated. Similarly, only a few studies have been conducted on feature selection for symbolic regression, but none of them addresses the incompleteness issue. In this work, a genetic programming-based method for simultaneous imputation and feature selection is developed. This method selects the predictive features for the incomplete features whilst constructing their imputation models. Such models are designed to be suitable for data sets with mixed numerical and categorical features. The performance of the proposed method is compared with state-of-the-art widely used imputation methods from three aspects: the imputation accuracy, the feature selection effectiveness, and the symbolic regression performance.