Enhancing Generalization in Evolutionary Feature Construction for Symbolic Regression through Vicinal Jensen Gap Minimization

TL;DR

This paper introduces a novel evolutionary feature construction method for symbolic regression that minimizes the vicinal Jensen gap to improve generalization and control overfitting, validated across numerous datasets.

Contribution

It proposes a new regularization approach based on vicinal Jensen gap minimization and a dynamic noise estimation strategy for better overfitting control in genetic programming.

Findings

Outperforms other complexity measures in experiments.

Achieves superior performance compared to 15 machine learning algorithms.

Effectively controls overfitting through Jensen gap minimization.

Abstract

Genetic programming-based feature construction has achieved significant success in recent years as an automated machine learning technique to enhance learning performance. However, overfitting remains a challenge that limits its broader applicability. To improve generalization, we prove that vicinal risk, estimated through noise perturbation or mixup-based data augmentation, is bounded by the sum of empirical risk and a regularization term-either finite difference or the vicinal Jensen gap. Leveraging this decomposition, we propose an evolutionary feature construction framework that jointly optimizes empirical risk and the vicinal Jensen gap to control overfitting. Since datasets may vary in noise levels, we develop a noise estimation strategy to dynamically adjust regularization strength. Furthermore, to mitigate manifold intrusion-where data augmentation may generate unrealistic samples that fall outside the data manifold-we propose a manifold intrusion detection mechanism. Experimental results on 58 datasets demonstrate the effectiveness of Jensen gap minimization compared to other complexity measures. Comparisons with 15 machine learning algorithms further indicate that genetic programming with the proposed overfitting control strategy achieves superior performance.