mumax: Function to find the maximal value of the penalty parameter...
In RKHSMetaMod: Ridge Group Sparse Optimization Problem for Estimation of a Meta Model Based on Reproducing Kernel Hilbert Spaces

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Calculates the value of the penalty parameter in the RKHS group lasso problem when the first penalized parameter group enters the model.

1	mu_max(Y, matZ)

`Y`	Vector of response observations of size n.
`matZ`	List of vMax components. Each component includes the eigenvalues and eigenvectors of the positive definite Gram matrices K_v, v=1,...,vMax. It should have the same format as the output "kv" of the function `calc_Kv`.

Details.

An object of type numeric is returned.

Note.

Halaleh Kamari

Kamari, H., Huet, S. and Taupin, M.-L. (2019) RKHSMetaMod : An R package to estimate the Hoeffding decomposition of an unknown function by solving RKHS Ridge Group Sparse optimization problem. <arXiv:1905.13695>

Meier, L. Van de Geer, S. and Buhlmann, P. (2008) The group LASSO for logistic regression. Journal of the Royal Statistical Society Series B. 70. 53-71. 10.1111/j.1467-9868.2007.00627.x.

calc_Kv

d <- 3
n <- 50
library(lhs)
X <- maximinLHS(n, d)
c <- c(0.2,0.6,0.8)
F <- 1;for (a in 1:d) F <- F*(abs(4*X[,a]-2)+c[a])/(1+c[a])
epsilon <- rnorm(n,0,1);sigma <- 0.2
Y <- F + sigma*epsilon
Dmax <- 3
kernel <- "matern"
Kv <- calc_Kv(X, kernel, Dmax, TRUE,TRUE)
matZ <- Kv$kv
mumax <- mu_max(Y, matZ)
mumax