Multidimensional Additive Spline Approximation

Jerome H. Friedman; Eric H. Grosse; Werner Stuetzle

doi:10.1137/0904023

Abstract

We describe an adaptive procedure that approximates a function of many variables by a sum of (univariate) spline functions $s_m $ of selected linear combinations $a_m \cdot x$ of the coordinates \[ \phi (x) = \sum_{1 \leqq m \leqq M} {s_m ( a_m \cdot x)}. \] The procedure is nonlinear in that not only the spline coefficients but also the linear combinations are optimized for the particular problem. The sample need not lie on a regular grid, and the approximation is affine invariant, smooth, and lends itself to graphical interpretation. Function values, derivatives, and integrals are inexpensive to evaluate.

Keywords

MathematicsSpline (mechanical)UnivariateAffine transformationNonlinear systemApplied mathematicsGridB-splineCombinatoricsMathematical analysisPure mathematicsGeometryMultivariate statisticsStatistics

Affiliated Institutions

Related Publications

Multivariate Smoothing Spline Functions

Dennis D. Cox

Given data $z_i = g(t_i ) + \varepsilon _i , 1 \leqq i \leqq n$, where g is the unknown function, the $t_i $ are known d-dimensional variables in a domain $\Omega $, and the $\v...

1984 SIAM Journal on Numerical Analysis 109 citations

Projection Pursuit Regression

Jerome H. Friedman , Werner Stuetzle

Abstract A new method for nonparametric multiple regression is presented. The procedure models the regression surface as a sum of general smooth functions of linear combinations...

1981 Journal of the American Statistical A... 473 citations

Compressed sensing

David L. Donoho

Suppose x is an unknown vector in Ropfm (a digital image or signal); we plan to measure n general linear functionals of x and then reconstruct. If x is known to be compressible ...

2004 17126 citations

A Class of Statistics with Asymptotically Normal Distribution

Wassily Hoeffding

Let $X_1, \\cdot, X_n$ be $n$ independent random vectors, $X_\\nu = (X^{(1)}_\\nu, \\cdots, X^{(r)}_\\nu),$ and $\\Phi(x_1, \\cdots, x_m)$ a function of $m(\\leq n)$ vectors $x_...

1948 The Annals of Mathematical Statistics 1829 citations

Robust Estimation of a Location Parameter

Peter J. Huber

This paper contains a new approach toward a theory of robust estimation; it treats in detail the asymptotic theory of estimating a location parameter for contaminated normal dis...

1964 The Annals of Mathematical Statistics 6618 citations

Publication Info

Year: 1983
Type: article
Volume: 4
Issue: 2
Pages: 291-301
Citations: 90
Access: Closed

External Links

Download PDF (Free) View on DOI.org Semantic Scholar

Social Impact

Altmetric

Multidimensional Additive Spline Approximation

PlumX Metrics

Social media, news, blog, policy document mentions

Citation Metrics

OpenAlex

Influential

CrossRef

Cite This

APA Style

                            
                                    Jerome H. Friedman, 
                                
                                    Eric H. Grosse, 
                                
                                    Werner Stuetzle
                                
                            (1983). 
                            Multidimensional Additive Spline Approximation. 
                            SIAM Journal on Scientific and Statistical Computing
                            , 4
                            (2)
                            , 291-301.
                            https://doi.org/10.1137/0904023

Identifiers

DOI: 10.1137/0904023

Data Quality

Data completeness: 81%