Identifying the mathematical relationships that best describe a dataset
remains a very challenging problem in machine learning, and is known as
Symbolic Regression (SR). In contrast to neural networks which are often
treated as black boxes, SR attempts to gain insight into the underlying
relationships between the independent variables and the target variable of a
given dataset by assembling analytical functions. In this paper, we present
GSR, a Generalized Symbolic Regression approach, by modifying the conventional
SR optimization problem formulation, while keeping the main SR objective
intact. In GSR, we infer mathematical relationships between the independent
variables and some transformation of the target variable. We constrain our
search space to a weighted sum of basis functions, and propose a genetic
programming approach with a matrix-based encoding scheme. We show that our GSR
method is competitive with strong SR benchmark methods, achieving promising
experimental performance on the well-known SR benchmark problem sets. Finally,
we highlight the strengths of GSR by introducing SymSet, a new SR benchmark set
which is more challenging relative to the existing benchmarks.

介绍了一种名为 GSR 的基于遗传编程的符号回归方法，该方法通过基函数的加权和发现自变量与目标变量之间的关系，并获得了与强符号回归基准方法相当的实验性能，并引入了一种新的符号回归基准集 SymSet。