ridgePgen.kCV.banded: K-fold cross-validated loglikelihood of ridge precision...

In porridge: Ridge-Type Penalized Estimation of a Potpourri of Models

K-fold cross-validated loglikelihood of ridge precision estimator for banded precisions.

Description

Function that calculates of the k-fold cross-validated negative (!) loglikelihood of the generalized ridge precision estimator, with a penalization that encourages a banded precision matrix.

Usage

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

Arguments

lambda	A numeric with the penalty parameter value.
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.
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.

Details

The penalty matrix \boldsymbol{\Lambda} is parametrized as follows. The elements of \boldsymbol{\Lambda} are (\boldsymbol{\Lambda})_{j,j'} = \lambda (| j - j'| + 1) for j, j' = 1, \ldots, p.

Value

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

Author(s)

W.N. van Wieringen.

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.banded(Y, 10^(-10), 10^(10),
                          target=matrix(0, p, p),
                          penalize.diag=FALSE, nInit=100, 
                          minSuccDiff=10^(-5)) 

# format the penalty matrix
lambdaOptMat <- matrix(NA, p, p)
for (j1 in 1:p){
    for (j2 in 1:p){
        lambdaOptMat[j1, j2] <- lambdaOpt * (abs(j1-j2)+1)
    }
}

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

porridge documentation built on Oct. 16, 2023, 1:06 a.m.