Multivariate adaptive regression splines. (English) Zbl 0765.62064

Friedman, Jerome H.

Ann. Stat. 19, No. 1, 1-141 (1991).

Summary: A new method is presented for flexible regression modeling of high dimensional data. The model takes the form of an expansion in product spline basis functions, where the number of basis functions as well as the parameters associated with each one (product degree and knot locations) are automatically determined by the data.
This procedure is motivated by the recursive partitioning approach to regression and shares its attractive properties. Unlike recursive partitioning, however, this method produces continuous models with continuous derivatives. It has more power and flexibility to model relationships that are nearly additive or involve interactions in at most a few variables. In addition, the model can be represented in a form that separately identifies the additive contributions and those associated with the different multivariable interactions.

MSC:

62J02	General nonlinear regression
62H99	Multivariate analysis
65D10	Numerical smoothing, curve fitting
65D07	Numerical computation using splines
65C99	Probabilistic methods, stochastic differential equations

Keywords:

nonparametric multiple regression; multivariable function approximation; statistical learning neural networks; multivariate smoothing; AID; CART; product degree; high dimensional data; expansion in product spline basis functions; knot locations; recursive partitioning approach to regression; continuous models; continuous derivatives