GP_NLS in Julia Documentation
Julia implementation of the GP-NLS algorithm for symbolic regression described in the paper:
What is Symbolic Regression?
Symbolic regression is the task of finding a good mathematical expression to describe the relationship between a set of independent variables$\mathbf{X} = X_1, X_2, \ldots, X_n$ with a dependent variable$Y$, normally represented as tabular data:
In other words, suppose that you have available$m$ observations with$n$ variables, and a response variable that you supose that have a relationship$f(\mathbf{X}) = Y$, but the function$f$ is unknown: we can only see how the response changes when the input changes, but we don't know how the response is described by the variables of the problem. Symbolic regression tries to find a function$\widehat{f}$ that approximates the output of the unknown function just by learning mathematical structures from the data itself.
How GP-NLS works
The idea behind the use of evolutionary algorithms is to manipulate a population of mathematical expressions computationally (represented using expression trees). A fitness function, which measures how good each expression is (this function could be, for example, the Mean Squared Error) the individuals of the population have their fitness to represent how well each function describes the data. Through variation operations (which define the power of exploration of the algorithm, done in the full search space, or the power of exploration, which performs a local search) and selective pressure (which promote the maintenance of good solutions in the population), a simulation of the evolutionary process tends to converge to good solutions present in the population. However, it is worth noting that there is no guarantee that the optimal solution will be found, although generally, the algorithm will return a good solution if possible.
The genetic programming algorithm starts with a random population of solutions, which are represented by trees, and then using a fitness function, it repeats the process of selecting the parents, performing the cross between them, applying a mutation on the child solutions, and, finally set a new generation choice between parents and children. This process is repeated until a stop criteria is met.
GP-NLS creates symbolic trees but expands them by adding an intercept, slope, and a coefficient to every variable. The new free parameters are then adjusted using the non-linear optimization method called Levenberg-Marquardt.
Functions visible by import
The functions that are exported are listed below.
Types
Default sets
Auxiliary functions
Genetic Programming algorithm
All functions
The module has some built-in auxiliary functions that its external use is not recommended. All implementations are listed in the modules of the library, but only some functions are exported outside the package.