GSR: A Generalized Symbolic Regression Approach

TL;DR

GSR introduces a generalized symbolic regression method that infers relationships between variables and transformed targets using a constrained search space and genetic programming, showing competitive performance on benchmarks.

Contribution

It proposes a novel GSR approach that modifies the SR optimization problem and introduces a new, more challenging benchmark set, SymSet.

Findings

GSR performs competitively on standard SR benchmarks.

GSR effectively infers relationships involving target transformations.

SymSet provides a more challenging benchmark for SR methods.

Abstract

Identifying the mathematical relationships that best describe a dataset remains a very challenging problem in machine learning, and is known as Symbolic Regression (SR). In contrast to neural networks which are often treated as black boxes, SR attempts to gain insight into the underlying relationships between the independent variables and the target variable of a given dataset by assembling analytical functions. In this paper, we present GSR, a Generalized Symbolic Regression approach, by modifying the conventional SR optimization problem formulation, while keeping the main SR objective intact. In GSR, we infer mathematical relationships between the independent variables and some transformation of the target variable. We constrain our search space to a weighted sum of basis functions, and propose a genetic programming approach with a matrix-based encoding scheme. We show that our GSR method is competitive with strong SR benchmark methods, achieving promising experimental performance on the well-known SR benchmark problem sets. Finally, we highlight the strengths of GSR by introducing SymSet, a new SR benchmark set which is more challenging relative to the existing benchmarks.