PS-Tree: A piecewise symbolic regression tree

Abstract

The symbolic methods have recently regained popularity due to their reasonable interpretability compared to neural network-based artificial intelligence techniques. The regression tree is such a symbolic method that divides the feature space into several subregions and builds a simple response surface model, such as a constant value or a linear model, for each subregion. However, this strategy may fail when nonlinear structures exist in the subregions. To overcome this problem, this paper proposes a new regression model, named piecewise symbolic regression tree (PS-Tree). Instead of using constant values or linear models as the leaf nodes, PS-Tree builds symbolic regressors for the leaf nodes or subregions. In addition to that, we also propose an adaptive space partition strategy by dynamically adjusting the partition of the space to alleviate the problem caused by incorrect partitioning. PS-Tree is applied to 122 synthetic and real-world datasets, and the results show that it outperforms several state-of-the-art regression methods.