Multivariate Adaptive Regression Splines

Publication	Friedman/91a: Multivariate Adaptive Regression Splines Hastie/Tibshirani/90a: Generalized Additive Models
Name	Multivariate Adaptive Regression Splines
Description	Adaptive regression splines (Friedman,1991) are a kind of additive models (Hastie and Tibshirani, 1990) that can be seen as a generalisation of regression trees introduced to overcome some of their limitations. Friedman (1991) describes these limitations in detail and shows how adaptive regression splines can overcome them. The resulting model is implemented in system MARS, which provides a regression model of the form, r(x) = c0 + p ∑ i=1 ci Ki ∏ k=1 [sk,i(Xv(k, i)-tk,i)]+ where, the are two-sided truncated power basis functions. This model can be recast into the more intuitive form given by, r(x) = c0 + ∑ fm(XM) + fm, n(XM, Xn) + ∑ fm, n, o (Xm, Xn, Xo) + ... In this equation the first sum is over all basis functions that involve only a single attribute. The second sum uses the basis functions involving two variables, and so on.
Method Type	Method