Reducing Overparameterization of Symbolic Regression Models with Equality Saturation

Overparameterized models in regression analysis are often harder to interpret and can be harder to fit because of ill-conditioning. Genetic programming is prone to overparameterized models as it evolves the structure of the model without taking the location of parameters into account. One way to alleviate this is rewriting the expression and merging the redundant fitting parameters. In this paper we propose the use of equality saturation to alleviate overparameterization. We first notice that all the tested GP implementations suffer from overparameterization to different extents and then show that equality saturation together with a small set of rewriting rules is capable of reducing the number of fitting parameters to a minimum with a high probability. Compared to one of the few available alternatives, Sympy, it produces much better and consistent results. These results lead to different possible future investigations such as the simplification of expressions during the evolutionary process, and improvement of the interpretability of symbolic models.