RKHSMetMod_qmax {RKHSMetaMod} | R Documentation |
Calculates the Gram matrices K_v
for a chosen kernel, determines \mu
, note \mu (qmax)
, for which the number of active groups in the RKHS group lasso solution is equal to qmax, and fits a solution of an RKHS ridge group sparse or an RKHS group lasso problem for each pair of penalty parameters (\mu (qmax),\gamma)
, in the Gaussian regression model.
RKHSMetMod_qmax(Y, X, kernel, Dmax, gamma, qmax, rat, Num, verbose)
Y |
Vector of response observations of size |
X |
Matrix of observations with |
kernel |
Character, indicates the type of the reproducing kernel: matern |
Dmax |
Integer, between |
gamma |
Vector of non negative scalars, values of the penalty parameter |
qmax |
Integer, shows the maximum number of active groups in the obtained solution. |
rat |
Positive scalar, to restrict the minimum value of |
Num |
Integer, it is used to restrict the number of different values of the penalty parameter |
verbose |
Logical, if TRUE, prints: the group |
Details.
List of three components "mus", "qs", and "MetaModel":
mus |
Vector, values of the evaluated penalty parameters |
qs |
Vector, number of active groups associated with each element in mus. |
MetaModel |
List with the same length as the vector gamma. Each component of the list is a list of |
mu |
Scalar, the value |
gamma |
Positive scalar, element of the input vector gamma associated with the estimated Meta-Model. |
Meta-Model |
An RKHS Ridge Group Sparse or RKHS Group Lasso object associated with the penalty parameters mu and gamma: |
intercept |
Scalar, estimated value of intercept. |
teta |
Matrix with vMax rows and |
fit.v |
Matrix with |
fitted |
Vector of size |
Norm.n |
Vector of size vMax, estimated values for the Ridge penalty norm. |
Norm.H |
Vector of size vMax, estimated values of the Sparse Group penalty norm. |
supp |
Vector of active groups. |
Nsupp |
Vector of the names of the active groups. |
SCR |
Scalar, equals to |
crit |
Scalar, indicates the value of penalized criteria. |
gamma.v |
Vector, coefficients of the Ridge penalty norm, |
mu.v |
Vector, coefficients of the Group Sparse penalty norm, |
iter |
List of two components: maxIter, and the number of iterations until the convergence is achieved. |
convergence |
TRUE or FALSE. Indicates whether the algorithm has converged or not. |
RelDiffCrit |
Scalar, value of the first convergence criteria at the last iteration, |
RelDiffPar |
Scalar, value of the second convergence criteria at the last iteration, |
For the case \gamma=0
the outputs "mu"=\mu_{g}
and "Meta-Model" is the same as the one returned by the function RKHSgrplasso
.
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>
calc_Kv
, mu_max
, RKHSgrplasso
, pen_MetMod
, grplasso_q
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"
gamma <- c(.5,.01,.001,0)
Num <- 10
rat <- 100
qmax <- 4
result <- RKHSMetMod_qmax(Y, X, kernel, Dmax, gamma, qmax, rat, Num,FALSE)
names(result)
result$mus
result$qs
l <- length(gamma)
for(i in 1:l){print(result$MetaModel[[i]]$mu)}
for(i in 1:l){print(result$MetaModel[[i]]$gamma)}
for(i in 1:l){print(result$MetaModel[[i]]$`Meta-Model`$Nsupp)}