mumax function

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

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

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.

Returns

An object of type numeric is returned.

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.

Author(s)

Halaleh Kamari

Note

Note.

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