Multivariate Adaptive Regression Splines

MARS is a form of regression analysis introduced by Jerome H. Friedman (1991), with the main purpose being to predict the values of a response variable from a set of predictor variables.

MARS is a nonparametric regression procedure that makes no assumption about the underlying functional relationship between the response and predictor variables.

This relationship is constructed from a set of coefficients and basis functions that are processed starting from the regression data. The method divides the input space into regions, each with its own regression equation. This makes MARS particularly suitable for problems with a large number of predictors. The following figure shows a distribution with two regression regions:

The MARS algorithm operates as a multiple piecewise linear regression, where each breakpoint (estimated from the data) defines the region of application for a very simple linear regression equation.

The general MARS model equation is as follows...