ridgeSIR {SISIR}

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)
## Not run: print(res_ridge)