kernel.pls.ic {plsdof} | R Documentation |
This function computes the optimal model parameters using three different model selection criteria (aic, bic, gmdl) and based on two different Degrees of Freedom estimates for PLS.
kernel.pls.ic(X, y, m = ncol(X), type = "vanilla", sigma = 1, step.size = 1)
X |
matrix of predictor observations. |
y |
vector of response observations. The length of y is the same as the number of rows of X .
|
m |
maximal number of Partial Least Squares components. Default is m=ncol(X) .
|
type |
type of kernel. type="vanilla" is a linear kernel. type="gaussian" is a gaussian kernel. Default is type="vanilla" .
|
sigma |
vector of kernel parameters. If type="gaussian" , these are the kernel widths. If the vanilla kernel is used,
sigma is not used. Default value is sigma=1 .
|
step.size |
After how many steps should the latent components be re-orthogonalized? See kernel.pls.fit for more details. Default is step.size=1 .
|
For the linear kernel (type="vanilla"
), we standardize X
to zero mean and unit variance. For the Gaussian kernel (type="gaussian"
), we normalize X
such that the range of each column is [-1,1].
The default value for sigma
is in general NOT a sensible parameter, and sigma
should always be selected from a RANGE of values. The default value for m
is a sensible upper bound only for the vanilla kernel.
DoF |
Degrees of Freedom |
m.aic |
optimal number of components for aic |
m.bic |
optimal number of components for bic |
m.gmdl |
optimal number of components for gmdl |
m.aic.naive |
optimal number of components for aic and the naive Degrees of Freedom |
m.bic.naive |
optimal number of components for bic and the naive Degrees of Freedom |
m.gmdl.naive |
optimal number of components for gmdl and the naive Degrees of Freedom |
sigma.aic |
optimal sigma for aic, only returned if type="gaussian" |
sigma.bic |
optimal sigma for bic, only returned if type="gaussian" |
sigma.gmdl |
optimal sigma for gmdl, only returned if type="gaussian" |
sigma.aic.naive |
optimal sigma for aic and the naive Degrees of Freedom, only returned if type="gaussian" |
sigma.bic.naive |
optimal sigma for bic and the naive Degrees of Freedom, only returned if type="gaussian" |
sigma.gmdl.naive |
optimal sigma for gmdl and the naive Degrees of Freedom, only returned if type="gaussian" |
Nicole Kraemer, Mikio L. Braun
Akaikie, H. (1973) "Information Theory and an Extension of the Maximum Likelihood Principle". Second International Symposium on Information Theory, 267 - 281.
Hansen, M., Yu, B. (2001). "Model Selection and Minimum Descripion Length Principle". Journal of the American Statistical Association, 96, 746 - 774
Kraemer, N., Braun, M.L. (2007) "Kernelizing PLS, Degrees of Freedom, and Efficient Model Selection", Proceedings of the 24th International Conference on Machine Learning, Omni Press, 441 - 448
Schwartz, G. (1979) "Estimating the Dimension of a Model" Annals of Statistics 26(5), 1651 - 1686.
n<-50 # number of observations p<-5 # number of variables X<-matrix(rnorm(n*p),ncol=p) y<-rnorm(n) # compute linear PLS linear.pls<-kernel.pls.ic(X,y,m=ncol(X))