M5GP: Parallel Multidimensional Genetic Programming with Multidimensional Populations for Symbolic Regression

Abstract

Machine learning and artificial intelligence are growing in popularity thanks to their ability to produce models that exhibit unprecedented performance in domains that include computer vision, natural language processing and code generation. However, such models tend to be very large and complex and impossible to understand using traditional analysis or human scrutiny. Conversely, Symbolic Regression methods attempt to produce models that are relatively small and (potentially) human-readable. In this domain, Genetic Programming (GP) has proven to be a powerful search strategy that achieves state-of-the-art performance. This paper presents a new GP-based feature transformation method called M5GP, which is hybridized with multiple linear regression to produce linear models, implemented to exploit parallel processing on graphical processing units for efficient computation. M5GP is the most recent variant from a family of feature transformation methods (M2GP, M3GP and M4GP) that have proven to be powerful tools for both classification and regression tasks applied to tabular data. The proposed method was evaluated on SRBench v2.0, the current standard benchmarking suite for Symbolic Regression. Results show that M5GP achieves performance that is competitive with the state-of-the-art, achieving a top-three rank on the most difficult subset of black-box problems. Moreover, it achieves the lowest computation time when compared to other GP-based methods that have similar accuracy scores.