Improving symbolic regression based on correlation between residuals and variables
Qi Chen, Bing Xue, Mengjie Zhang · 2020
In traditional regression analysis, a detailed examination of the residuals can provide an important way of validating the model quality. However, it has not been utilised in genetic programming based symbolic regression. This work aims to fill this gap and propose a new evaluation criterion of minimising the correlation between the residuals of regression models and the independent variables. Based on a recent association detection measure, maximal information coefficient which provides an accurate estimation of the correlation, the new evaluation measure is expected to enhance the generalisation of genetic programming by driving the evolutionary process towards models that are without unnecessary complexity and less likely learning from noise in data. The experiment results show that, compared with standard genetic programming which selects model based on the training error only and two state-of-the-art multiobjective genetic programming methods with mechanisms to prefer models with adequate structures, our new multiobjective genetic programming method minimising both the correlation between residuals and variable, and the training error has a consistently better generalisation performance and evolves simpler models.