Exhaustive Symbolic Regression Function Sets

ESR (Exhaustive Symbolic Regression) is a symbolic regression algorithm which efficiently and systematically finds all possible equations at fixed complexity (defined to be the number of nodes in its tree representation) given a set of basis functions. This is achieved by identifying the unique equations, so that one minimises the number of equations which one would have to fit to data. Here we provide the functions generated, the unique equations, and the mappings between all equations and unique ones using different sets of basis functions. These are: "core_maths": \(\{x, a, {\rm inv}, +, -, \times, \div, {\rm pow} \}\) "ext_maths": \(\{x, a, {\rm inv}, \sqrt{\cdot}, {\rm square}, \exp, +, -, \times, \div, {\rm pow} \}\) where \(x\) is the input variable and \(a\) denotes a constant. One can fit these functions to a data set of interest by using the ESR package.ESR（穷举符号回归，Exhaustive Symbolic Regression）是一种符号回归（Symbolic Regression）算法，可在给定一组基函数的前提下，高效且系统地枚举固定复杂度（定义为其树状表示（tree representation）中的节点数目）下的所有可能方程。该算法通过识别唯一方程来实现这一目标，从而最小化需拟合至数据集的方程总量。本数据集提供了生成的函数、唯一方程，以及使用不同基函数集时，全体方程与唯一方程之间的映射关系。具体包含两类基函数集："core_maths": {x, a, inv, +, -, ×, ÷, pow}；"ext_maths": {x, a, inv, √·, square, exp, +, -, ×, ÷, pow}。其中x为输入变量，a表示常数。用户可通过ESR软件包将这些函数拟合至目标数据集。