Symbolic Regression with Fast Function Extraction and Nonlinear Least Squares Optimization

Abstract: Fast Function Extraction (FFX) is a deterministic algorithm for solving symbolic regression problems. We improve the accuracy of FFX by adding parameters to the arguments of nonlinear functions. Instead of only optimizing linear parameters, we optimize these additional nonlinear parameters with separable nonlinear least squared optimization using a variable projection algorithm. Both FFX and our new algorithm is applied on the PennML benchmark suite. We show that the proposed extensions of FFX leads to higher accuracy while providing models of similar length and with only a small increase in runtime on the given data. Our results are compared to a large set of regression methods that were already published for the given benchmark suite.