ridgeSIR: ridge SIR

In SISIR: Select Intervals Suited for Functional Regression

ridge SIR

Description

ridgeSIR performs the first step of the method (ridge regularization of SIR)

Usage

ridgeSIR(x, y, H, d, mu2 = NULL)

Arguments

x	explanatory variables (numeric matrix or data frame)
y	target variable (numeric vector)
H	number of slices (integer)
d	number of dimensions to be kept
mu2	ridge regularization parameter (numeric, positive)

Details

SI-SIR

Value

S3 object of class ridgeRes: a list consisting of

EDR

the estimated EDR space (a p x d matrix)

condC

the estimated slice projection on EDR (a d x H matrix)

eigenvalues

the eigenvalues obtained during the generalized eigendecomposition performed by SIR

parameters

a list of hyper-parameters for the method:

H

number of slices

d

dimension of the EDR space

mu2

regularization parameter for the ridge penalty

utils

useful outputs for further computations:

Sigma

covariance matrix for x

slices

slice number for all observations

invsqrtS

value of the inverse square root of the regularized covariance matrix for x

Author(s)

Victor Picheny, [e-mail]
Remi Servien, [e-mail]
Nathalie Vialaneix, [e-mail]

References

Picheny, V., Servien, R. and Villa-Vialaneix, N. (2019) Interpretable sparse SIR for digitized functional data. Statistics and Computing, 29(2), 255–267.

See Also

sparseSIR, SISIR, tune.ridgeSIR

Examples

set.seed(1140)
tsteps <- seq(0, 1, length = 50)
simulate_bm <- function() return(c(0, cumsum(rnorm(length(tsteps)-1, sd=1))))
x <- t(replicate(50, simulate_bm()))
beta <- cbind(sin(tsteps*3*pi/2), sin(tsteps*5*pi/2)) 
y <- log(abs(x %*% beta[ ,1])) + sqrt(abs(x %*% beta[ ,2]))
y <- y + rnorm(50, sd = 0.1)
res_ridge <- ridgeSIR(x, y, H = 10, d = 2, mu2 = 10^8)
res_ridge

SISIR documentation built on Sept. 11, 2024, 7:40 p.m.