gmdl {plsdof}R Documentation

Generalized minimum description length

Description

This function computes the optimal parameter set based on the generalized minimum description length.

Usage

gmdl(RSS, n, DoF, yhat)

Arguments

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

Details

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.

Value

The function returns a vector of length 2 that contains the row and column index of the gmdl-optimal model

Author(s)

Nicole Kraemer, Mikio L. Braun

References

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

See Also

information.criteria, kernel.pls.ic, aic, bic

Examples

## This is an internal function.

[Package plsdof version 0.1-1 Index]