The Annals of Statistics

Multivariate Adaptive Regression Splines

Jerome H. Friedman

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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.

Article information

Ann. Statist. Volume 19, Number 1 (1991), 1-67.

First available in Project Euclid: 12 April 2007

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Zentralblatt MATH identifier


Primary: 62J02: General nonlinear regression
Secondary: 65D07: Splines 65D10: Smoothing, curve fitting 65D15: Algorithms for functional approximation 68T05: Learning and adaptive systems [See also 68Q32, 91E40] 93E14: Data smoothing 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20] 68T10: Pattern recognition, speech recognition {For cluster analysis, see 62H30} 90A19 93C35: Multivariable systems 93E11: Filtering [See also 60G35]

Nonparametric multiple regression multivariable function approximation statistical learning neural networks multivariate smoothing splines recursive partitioning AID CART


Friedman, Jerome H. Multivariate Adaptive Regression Splines. Ann. Statist. 19 (1991), no. 1, 1--67. doi:10.1214/aos/1176347963.

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