optPenalty.kCVauto {rags2ridges} | R Documentation |
Automatic search for optimal penalty parameter
Description
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.
Usage
optPenalty.kCVauto(
Y,
lambdaMin,
lambdaMax,
lambdaInit = (lambdaMin + lambdaMax)/2,
fold = nrow(Y),
cor = FALSE,
target = default.target(covML(Y)),
type = "Alt"
)
Arguments
Y |
Data |
lambdaMin |
A |
lambdaMax |
A |
lambdaInit |
A |
fold |
A |
cor |
A |
target |
A target |
type |
A |
Details
The function determines the optimal value of the penalty parameter by
application of the Brent algorithm (1971) to the K
-fold
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 K
-fold cross-validated negative log-likelihood
score is minimized is deemed optimal. The function employs the Brent
algorithm as implemented in the
optim
function.
Value
An object of class list
:
optLambda |
A |
optPrec |
A
|
Note
When cor = TRUE
correlation matrices are used in the
computation of the (cross-validated) negative log-likelihood score, i.e.,
the K
-fold 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.
Under the default setting of the fold-argument, fold = nrow(Y)
, one
performes leave-one-out cross-validation.
Author(s)
Wessel N. van Wieringen, Carel F.W. Peeters <carel.peeters@wur.nl>
References
Brent, R.P. (1971). An Algorithm with Guaranteed Convergence for Finding a Zero of a Function. Computer Journal 14: 422-425.
See Also
GGMblockNullPenalty
, GGMblockTest
,
ridgeP
, optPenalty.aLOOCV
,
optPenalty.kCV
,
default.target
,
covML
Examples
## 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 using K = n
OPT <- optPenalty.kCVauto(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.kCVauto(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 penalty
## Another example using K = 5
OPT <- optPenalty.kCVauto(X, lambdaMin = .001, lambdaMax = 30, fold = 5); OPT
OPT$optLambda # Optimal penalty
OPT$optPrec # Regularized precision under optimal penalty