Enhancing Generalization in Evolutionary Feature Construction for Symbolic Regression Through Vicinal Jensen Gap Minimization
This work addresses the limited generalization of genetic programming in symbolic regression due to overfitting. The authors propose a novel evolutionary feature construction method based on neighborhood risk decomposition, which, for the first time, incorporates the neighborhood Jensen gap as a regularization term to jointly optimize empirical risk and the Jensen gap. To enhance robustness, the approach integrates dynamic regularization strength adjustment, manifold intrusion detection, and noise perturbation mechanisms, effectively mitigating the generation of unrealistic samples caused by data augmentation. Extensive experiments on 58 benchmark datasets demonstrate that the proposed method outperforms existing complexity-controlling metrics and significantly improves symbolic regression performance compared to 15 state-of-the-art machine learning algorithms.