Data-Informed Model Complexity Metric for Optimizing Symbolic Regression Models

Choosing models from a well-fitted evolved population that generalizes beyond training data is difficult. We introduce a pragmatic method to estimate model complexity using Hessian rank for post-processing selection. Complexity is approximated by averaging the model output Hessian rank across a few points (N=3), offering efficient and accurate rank estimates. This method aligns model selection with input data complexity, calculated using intrinsic dimensionality (ID) estimators. Using the StackGP system, we develop symbolic regression models for the Penn Machine Learning Benchmark and employ twelve scikit-dimension library methods to estimate ID, aligning model expressiveness with dataset ID. Our data-informed complexity metric finds the ideal complexity window, balancing model expressiveness and accuracy, enhancing generalizability without bias common in methods reliant on user-defined parameters, such as parsimony pressure in weight selection.