Multivariate Adaptive Regression Splines

Multivariate adaptive regression splines (MARS) is a regression technique used to model relationships between predictor variables and a dependent variable.

MARS is used when the relationship between predictor variables and the dependent variable is thought to vary over its value range. It is particularly useful in scenarios where the relationship is non-linear and involves interactions between variables.

MARS works by creating a set of basis functions, primarily hinge functions, which are combined to model the data. A hinge function has the form max(0, x-c), where c is a knot, making the function relevant only for values of x greater than c. The model is built using a stepwise regression approach, adding predictor variables with candidate knots one by one. MARS includes a pruning step to remove basis functions that do not significantly contribute to the model’s accuracy, helping to prevent overfitting.

For example, in predicting air humidity based on temperature, the relationship changes significantly at the boiling point of water. MARS can capture this change by introducing a knot at 100 degrees Celsius.

As the name MARS may be protected by trademark laws, many open-source implementations refer to this algorithm as Earth.

In summary, MARS is a powerful tool for modeling complex, non-linear relationships in data. It requires more training data than simple regression methods but offers flexibility and robustness in capturing variable interactions.