Thinking Outside the Template with Modular GP-GOMEA

Abstract

The goal in Symbolic Regression (SR) is to discover expressions that accurately map input to output data. Because often the intent is to understand these expressions, there is a trade-off between accuracy and the interpretability of expressions. GP-GOMEA excels at producing small SR expressions (increasing the potential for interpretability) with high accuracy, but requires a fixed tree template, which limits the types of expressions that can be evolved. This paper presents a modular representation for GP-GOMEA that allows multiple trees to be evolved simultaneously that can be used as (functional) subexpressions. While each tree individually is constrained to a (small) fixed tree template, the final expression, if expanded, can exhibit a much larger structure. Furthermore, the use of subexpressions decomposes the original regression problem and opens the possibility for enhanced interpretability through the piece-wise understanding of small subexpressions. We compare the performance of GP-GOMEA with and without modular templates on a variety of datasets. We find that our proposed approach generally outperforms single-template GP-GOMEA and can moreover uncover ground-truth expressions underlying synthetic datasets with modular subexpressions at a faster rate than GP-GOMEA without modular subexpressions.