SAGE-Fit: New Method Improves Symbolic Regression Parameter Optimization
A novel approach known as SAGE-Fit (Structure-Aware and Semantics-Guided Evaluator for Symbolic Regression) tackles the issue of 'Good Structure, Bad Score' in symbolic regression. This challenge arises when valid equation structures receive low scores due to subpar parameter optimization. Symbolic regression operates through a bi-level optimization framework: the outer loop identifies discrete equation structures, while the inner loop fine-tunes continuous parameters. The presence of nonlinear operators complicates the inner loop, making it highly non-convex. Budget limitations often necessitate the use of rapid local solvers like BFGS, which can produce poor local minima and miscalculate scores for valid structures, diverting the outer loop from the correct equation. SAGE-Fit serves as an SR-native evaluator, aiming to enhance parameter fitting quality and boost the effectiveness and precision of symbolic regression. The research is accessible on arXiv with the reference 2605.23272.
Key facts
- Symbolic regression distills mathematical equations from observational data.
- Most SR methods use a bi-level optimization framework.
- The outer loop searches for discrete equation structure.
- The inner loop optimizes continuous parameters.
- Nonlinear operators make the inner loop highly non-convex.
- Fast local solvers like BFGS often yield poor local minima.
- The 'Good Structure, Bad Score' phenomenon misguides the search.
- SAGE-Fit is proposed to resolve this bottleneck.
Entities
Institutions
- arXiv