Genetic Programming with Noise Sensitivity for Imputation Predictor Selection in Symbolic Regression with Incomplete Data

This paper presents a feature selection method that incorporates a sensitivity-based single feature importance measure in a context-based feature selection approach. The single-wise importance is based on the sensitivity of the learning performance with respect to adding noise to the predictive features. Genetic programming is used as a context-based selection mechanism, where the selection of features is determined by the change in the performance of the evolved genetic programming models when the feature is injected with noise. Imputation is a key strategy to mitigate the data incompleteness problem. However, it has been rarely investigated for symbolic regression on incomplete data. In this work, an attempt to contribute to filling this gap is presented. The proposed method is applied to selecting imputation predictors (features/variables) in symbolic regression with missing values. The evaluation is performed on real-world data sets considering three performance measures: imputation accuracy, symbolic regression performance, and features’ reduction ability. Compared with the benchmark methods, the experimental evaluation shows that the proposed method can achieve an enhanced imputation, improve the symbolic regression performance, and use smaller sets of selected predictors.