In this paper we consider the problem of learning a regression function without assuming its functional form. This problem is referred to as symbolic regression. An expression tree is typically used to represent a solution function, which is determined by assigning operators and operands to the nodes. The symbolic regression problem can be formulated as a nonconvex mixed-integer nonlinear program (MINLP), where binary variables are used to assign operators and nonlinear expressions are used to propagate data values through nonlinear operators such as square, square root, and exponential. We extend this formulation by adding new cuts that improve the solution of this challenging MINLP. We also propose a heuristic that iteratively builds an expression tree by solving a restricted MINLP. We perform computational experiments and compare our approach with a mixed-integer program-based method and a neural-network-based method from the literature.

翻译：在本文中, 我们考虑的是学习回归函数而不使用其功能形式的问题。 这个问题被称为象征性回归。 表达树通常用来代表一个解决方案功能, 由指定操作员和操作员到节点来决定。 象征性回归问题可以作为一个非convex混合整数非线性程序( MINLP ) 来表达, 该程序使用二进制变量来分配操作员, 并且使用非线性表达式来通过非线性操作员( 如平方、 平方根和指数化)来传播数据值。 我们通过添加新的削减来扩展这一公式, 从而改进这个挑战性 MINLP 的解决方案。 我们还提出一种反复构建表达树的杂念, 通过解决一个受限制的 MINLP 。 我们进行计算实验, 并将我们的方法与基于混合整数程序的方法和文献基于神经网络的方法进行比较 。