Automatic search for optimal penalty parameter
This function is now deprecated. Please use optPenalty.kCVauto
instead.
optPenalty.LOOCVauto( Y, lambdaMin, lambdaMax, lambdaInit = (lambdaMin + lambdaMax)/2, cor = FALSE, target = default.target(covML(Y)), type = "Alt" )
Y |
Data |
lambdaMin |
A |
lambdaMax |
A |
lambdaInit |
A |
cor |
A |
target |
A target |
type |
A |
Function that performs an 'automatic' search for the optimal penalty
parameter for the ridgeP call by employing Brent's method to
the calculation of a cross-validated negative log-likelihood score.
The function determines the optimal value of the penalty parameter by application of the Brent algorithm (1971) to the (leave-one-out) cross-validated negative log-likelihood score (using a regularized ridge estimator for the precision matrix). The search for the optimal value is automatic in the sense that in order to invoke the root-finding abilities of the Brent method, only a minimum value and a maximum value for the penalty parameter need to be specified as well as a starting penalty value. The value at which the (leave-one-out) cross-validated negative log-likelihood score is minimized is deemed optimal. The function employs the Brent algorithm as implemented in the optim function.
An object of class list:
optLambda |
A |
optPrec |
A
|
When cor = TRUE correlation matrices are used in the
computation of the (cross-validated) negative log-likelihood score, i.e.,
the leave-one-out sample covariance matrix is a matrix on the correlation
scale. When performing evaluation on the correlation scale the data are
assumed to be standardized. If cor = TRUE and one wishes to used the
default target specification one may consider using target =
default.target(covML(Y, cor = TRUE)). This gives a default target under the
assumption of standardized data.
Wessel N. van Wieringen, Carel F.W. Peeters <cf.peeters@vumc.nl>
Brent, R.P. (1971). An Algorithm with Guaranteed Convergence for Finding a Zero of a Function. Computer Journal 14: 422-425.
## Obtain some (high-dimensional) data
p = 25
n = 10
set.seed(333)
X = matrix(rnorm(n*p), nrow = n, ncol = p)
colnames(X)[1:25] = letters[1:25]
## Obtain regularized precision under optimal penalty
OPT <- optPenalty.LOOCVauto(X, lambdaMin = .001, lambdaMax = 30); OPT
OPT$optLambda # Optimal penalty
OPT$optPrec # Regularized precision under optimal penalty
## Another example with standardized data
X <- scale(X, center = TRUE, scale = TRUE)
OPT <- optPenalty.LOOCVauto(X, lambdaMin = .001, lambdaMax = 30, cor = TRUE,
target = default.target(covML(X, cor = TRUE))); OPT
OPT$optLambda # Optimal penalty
OPT$optPrec # Regularized precision under optimal penaltyPlease choose more modern alternatives, such as Google Chrome or Mozilla Firefox.