mu_max {RKHSMetaMod}

Function to find the maximal value of the penalty parameter in the RKHS Group Lasso problem.

Description

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

Usage

mu_max(Y, matZ)

Arguments

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

Details.

Value

An object of type numeric is returned.

Note

Note.

Author(s)

Halaleh Kamari

References

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.

See Also

calc_Kv

Examples

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