gmdl {plsdof} | R Documentation |
This function computes the optimal parameter set based on the generalized minimum description length.
gmdl(RSS, n, DoF, yhat)
RSS |
matrix of residual sum of squares. The columns correspond to the number of latent components for PLS, and the rows correspond to the different kernel parameters. If the vanilla kernel is used, RSS consists of one row. For a Gaussian kernel, each row corresponds to a sigma value. |
n |
number of observations. |
DoF |
Degrees of Freedom. The size of DoF is the same as the size of RSS .
|
yhat |
matrix of squared norm of yhat. The size of yhat is the same as the size of RSS
|
The gmdl criterion is defined as
gmdl=\frac{n}{2}log(S)+\frac{DoF}{2}log(F)+\frac{1}{2}log(n)
with
S=\frac{RSS}{n-DoF}
and
F=\frac{\|\hat y\|^ 2}{DoF\cdot S}
Note that it is also possible to use this function for other regression methods than Partial Least Squares.
The function returns a vector of length 2 that contains the row and column index of the gmdl-optimal model
Nicole Kraemer, Mikio L. Braun
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
information.criteria
, kernel.pls.ic
, aic
, bic
## This is an internal function.