Transformation-Interaction-Rational Representation for Symbolic Regression

TL;DR

This paper introduces the Transformation-Interaction-Rational representation for symbolic regression, enhancing approximation power while maintaining interpretability, and demonstrates its effectiveness through genetic programming experiments on benchmark datasets.

Contribution

It extends the Interaction-Transformation representation by incorporating rational functions, improving model expressiveness in symbolic regression.

Findings

Significant performance improvement over previous methods

State-of-the-art results on benchmark datasets

Enhanced approximation capabilities with controlled complexity

Abstract

Symbolic Regression searches for a function form that approximates a dataset often using Genetic Programming. Since there is usually no restriction to what form the function can have, Genetic Programming may return a hard to understand model due to non-linear function chaining or long expressions. A novel representation called Interaction-Transformation was recently proposed to alleviate this problem. In this representation, the function form is restricted to an affine combination of terms generated as the application of a single univariate function to the interaction of selected variables. This representation obtained competing solutions on standard benchmarks. Despite the initial success, a broader set of benchmarking functions revealed the limitations of the constrained representation. In this paper we propose an extension to this representation, called Transformation-Interaction-Rational representation that defines a new function form as the rational of two Interaction-Transformation functions. Additionally, the target variable can also be transformed with an univariate function. The main goal is to improve the approximation power while still constraining the overall complexity of the expression. We tested this representation with a standard Genetic Programming with crossover and mutation. The results show a great improvement when compared to its predecessor and a state-of-the-art performance for a large benchmark.