A Symbolic Hessian-Based Approach for Assessing Model Complexity in Symbolic Regression

In this work, we develop a novel method for estimating model curvature to be used in model selection and evaluation in symbolic regression by symbolically evaluating the model's Hessian matrix at the maximum, minimum, and median points with respect to the response surface. We demonstrate that this estimator is unique from previous methods for computing model complexity and demonstrate that it is relatively computationally efficient. We further validate the method by showcasing that the estimator ranks equations in line with expectations while also exploring the impact of using the max, min, and median points as the references for assessing a model's curvature. Finally, we explore how the metric impacts evolutionary search when used during selection.