Symbolic regression is a nonparametric, evolutionary optimization method for identifying mathematical models in the form of symbolic expressions, aiming to find a function \( f \) that approximates a set of data points \( (x_i, y_i) \) as accurately as possible.
Formally, the search is defined as an optimization problem:
\[ \min_{f \in \mathcal{F}} \sum_{i=1}^n (y_i - f(x_i))^2 + \lambda \cdot ext{Complexity}(f) \]
where \( \mathcal{F} \) is the space of all possible expressions composed of predefined operators (e.g., \( +, -, imes, \div, \sin, \log \)) and variables, and \( \lambda \) is a regularization parameter controlling model complexity.
The optimization is usually performed using genetic programming, which generates, evaluates, and evolves populations of formulas through selection, crossover, and mutation.
Symbolic regression often produces interpretable models that represent physical or system-theoretical relationships and is used in fields such as system identification, science, and engineering.
Definition:
“Symbolic regression is an evolutionary learning method that, by searching a space of possible mathematical expressions, finds an equation that describes data while balancing model accuracy and complexity.”
Source:
Koza, J. R. (1992). Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press.