Automatic feature engineering for regression models with machine learning: An evolutionary computation and statistics hybrid

Abstract Symbolic Regression (SR) is a well-studied task in Evolutionary Computation (EC), where adequate free-form mathematical models must be automatically discovered from observed data. Statisticians, engineers, and general data scientists still prefer traditional regression methods over EC methods because of the solid mathematical foundations, the interpretability of the models, and the lack of randomness, even though such deterministic methods tend to provide lower quality prediction than stochastic EC methods. On the other hand, while EC solutions can be big and uninterpretable, they can be created with less bias, finding high-quality solutions that would be avoided by human researchers. Another interesting possibility is using EC methods to perform automatic feature engineering for a deterministic regression method instead of evolving a single model; this may lead to smaller solutions that can be easy to understand. In this contribution, we evaluate an approach called Kaizen Programming (KP) to develop a hybrid method employing EC and Statistics. While the EC method builds the features, the statistical method efficiently builds the models, which are also used to provide the importance of the features; thus, features are improved over the iterations resulting in better models. Here we examine a large set of benchmark SR problems known from the EC literature. Our experiments show that KP outperforms traditional Genetic Programming - a popular EC method for SR - and also shows improvements over other methods, including other hybrids and well-known statistical and Machine Learning (ML) ones. More in line with ML than EC approaches, KP is able to provide high-quality solutions while requiring only a small number of function evaluations.