porridge (version 0.3.3)

ridgePgen.kCV.groups: K-fold cross-validated loglikelihood of ridge precision estimator with group-wise penalized variates.

Description

Function that calculates of the k-fold cross-validated negative (!) loglikelihood of the generalized ridge precision estimator, assuming that variates are grouped and penalized group-wise.

Usage

ridgePgen.kCV.groups(lambdaGrps, Y, fold=nrow(Y), 
                     groups, target, 
                     zeros=matrix(nrow=0, ncol=2), 
                     penalize.diag=TRUE, nInit=100, 
                     minSuccDiff=10^(-5))

Value

The function returns a numeric containing the cross-validated negative loglikelihood.

Arguments

lambdaGrps

A numeric with penalty parameter values, one per group. Values should be specified in the same order as the first appearance of a group representative.

Y

Data matrix with samples as rows and variates as columns.

fold

A numeric or integer specifying the number of folds to apply in the cross-validation.

groups

Anumeric indicating to which group a variate belongs. Same values indicate same group.

target

A semi-positive definite target matrix towards which the estimate is shrunken.

zeros

A two-column matrix, with the first and second column containing the row- and column-index of zero precision elements.

penalize.diag

A logical indicating whether the diagonal should be penalized.

nInit

A numeric specifying the number of iterations.

minSuccDiff

A numeric: minimum successive difference (in terms of their penalized loglikelihood) between two succesive estimates to be achieved.

Author

W.N. van Wieringen.

Details

The penalty matrix \(\boldsymbol{\Lambda}\) is parametrized as follows. The elements of \(\boldsymbol{\Lambda}\) are \((\boldsymbol{\Lambda})_{j,j'} = \frac{1}{2} (\lambda_k + \lambda_{k'})\) for \(j, j' = 1, \ldots, p\) if \(j\) and \(j'\) belong to groups \(k\) and \(k'\), respectively, where \(\lambda_k\) and \(\lambda_{k'}\) are the corresponding group-specific penalty parameters.

References

van Wieringen, W.N. (2019), "The generalized ridge estimator of the inverse covariance matrix", Journal of Computational and Graphical Statistics, 28(4), 932-942.

See Also

ridgePgen

Examples

# set dimension and sample size
p <- 10
n <- 10

# penalty parameter matrix
lambda       <- matrix(1, p, p)
diag(lambda) <- 0.1

# generate precision matrix
Omega       <- matrix(0.4, p, p)
diag(Omega) <- 1
Sigma       <- solve(Omega)

# data 
Y <- mvtnorm::rmvnorm(n, mean=rep(0,p), sigma=Sigma)
S <- cov(Y)

# find optimal penalty parameters through cross-validation
lambdaOpt <- optPenaltyPgen.kCVauto.groups(Y, rep(10^(-10), 2), rep(10^(10), 2), 
                          groups=c(rep(0, p/2), rep(1, p/2)), 
                          target=matrix(0, p, p),
                          penalize.diag=FALSE, nInit=100, 
                          minSuccDiff=10^(-5)) 

# format the penalty matrix
lambdaOptVec <- c(rep(lambdaOpt[1], p/2), rep(lambdaOpt[2], p/2))
lambdaOptMat <- outer(lambdaOptVec, lambdaOptVec, "+")

# generalized ridge precision estimate
Phat <- ridgePgen(S, lambdaOptMat, matrix(0, p, p))