Elite Bases Regression: A Real-time Algorithm for Symbolic Regression

TL;DR

Elite Bases Regression (EBR) is a new real-time, non-evolutionary algorithm for symbolic regression that efficiently constructs models by iteratively selecting elite basis functions based on correlation, outperforming some existing methods.

Contribution

The paper introduces EBR, a novel non-evolutionary approach for symbolic regression that improves speed and effectiveness over traditional genetic programming methods.

Findings

EBR outperforms FFX in solving symbolic regression problems.

EBR constructs models using elite basis functions based on correlation.

The method is suitable for large-scale problems with many variables.

Abstract

Symbolic regression is an important but challenging research topic in data mining. It can detect the underlying mathematical models. Genetic programming (GP) is one of the most popular methods for symbolic regression. However, its convergence speed might be too slow for large scale problems with a large number of variables. This drawback has become a bottleneck in practical applications. In this paper, a new non-evolutionary real-time algorithm for symbolic regression, Elite Bases Regression (EBR), is proposed. EBR generates a set of candidate basis functions coded with parse-matrix in specific mapping rules. Meanwhile, a certain number of elite bases are preserved and updated iteratively according to the correlation coefficients with respect to the target model. The regression model is then spanned by the elite bases. A comparative study between EBR and a recent proposed machine learning method for symbolic regression, Fast Function eXtraction (FFX), are conducted. Numerical results indicate that EBR can solve symbolic regression problems more effectively.