Introns and Templates Matter: Rethinking Linkage in GP-GOMEA

TL;DR

This paper improves GP-GOMEA for symbolic regression by introducing new linkage learning measures that account for introns and leverage template structures, leading to better performance and more interpretable solutions.

Contribution

It proposes two novel linkage learning measures for GP-GOMEA, explicitly considering introns and template structures, enhancing its effectiveness in symbolic regression.

Findings

Both new measures improve GP-GOMEA performance across five problems.

The learned linkage closely matches the template structure.

Using template-based linkage yields the best results.

Abstract

GP-GOMEA is among the state-of-the-art for symbolic regression, especially when it comes to finding small and potentially interpretable solutions. A key mechanism employed in any GOMEA variant is the exploitation of linkage, the dependencies between variables, to ensure efficient evolution. In GP-GOMEA, mutual information between node positions in GP trees has so far been used to learn linkage. For this, a fixed expression template is used. This however leads to introns for expressions smaller than the full template. As introns have no impact on fitness, their occurrences are not directly linked to selection. Consequently, introns can adversely affect the extent to which mutual information captures dependencies between tree nodes. To overcome this, we propose two new measures for linkage learning, one that explicitly considers introns in mutual information estimates, and one that revisits linkage learning in GP-GOMEA from a grey-box perspective, yielding a measure that needs not to be learned from the population but is derived directly from the template. Across five standard symbolic regression problems, GP-GOMEA achieves substantial improvements using both measures. We also find that the newly learned linkage structure closely reflects the template linkage structure, and that explicitly using the template structure yields the best performance overall.