pseudo.bases: Generate pseudo-spline bases
In gamsel: Fit Regularization Path for Generalized Additive Models

Description Usage Arguments Details Value Author(s) References Examples

View source: R/pseudo.bases.R

Generate an approximation to the Demmler-Reinsch orthonormal bases for smoothing splines, using orthogonal polynomials. basis.gen generates a basis for a single x, and pseudo.bases generates a list of bases for each column of the matrix x.

1	pseudo.bases(x, degree = 8, df = 6, parallel = FALSE, ...)

`x`	A vector of values for `basis.gen`, or a matrix for `pseudo.bases`
`degree`	The nominal number of basis elements. The basis returned has no more than `degree` columns. For `pseudo.bases` this can be a single value or a vector of values, which are recycled sequentially for each column of `x`
`df`	The degrees of freedom of the smoothing spline.
`parallel`	if TRUE, parallelize
`...`	other arguments for `basis.gen` can be passed through to `[basis.gen]`

basis.gen starts with a basis of orthogonal polynomials of total degree. These are each smoothed using a smoothing spline, which allows for a one-step approximation to the Demmler-Reinsch basis for a smoothing spline of rank equal to the degree. See the reference for details. The function also approximates the appropriate diagonal penalty matrix for this basis, so that the a approximate smoothing spline (generalized ridge regression) has the target df.

An orthonormal basis is returned (a list for pseudo.bases). This has an attribute parms, which has elements coefsCoefficients needed to generate the orthogonal polynomials rotateTransformation matrix for transforming the polynomial basis dpenalty values for the diagonal penalty dfdf used degreenumber of columns

Alexandra Chouldechova and Trevor Hastie
Maintainer: Trevor Hastie hastie@stanford.edu

T. Hastie Pseudosplines. (1996) JRSSB 58(2), 379-396.
Chouldechova, A. and Hastie, T. (2015) Generalized Additive Model Selection

##data=gamsel:::gendata(n=500,p=12,k.lin=3,k.nonlin=3,deg=8,sigma=0.5)
data = readRDS(system.file("extdata/gamsel_example.RDS", package = "gamsel"))
attach(data)
bases=pseudo.bases(X,degree=10,df=6)
## Not run: 
     require(doMC)
     registerDoMC(cores=4)
     bases=pseudo.bases(X,degree=10,df=6,parallel=TRUE)

## End(Not run)