Kernel Partial Least Squares Fit

This function computes the Partial Least Squares fit. This algorithm scales mainly in the number of observations.

Usage

kernel.pls.fit(
  X,
  y,
  m = ncol(X),
  compute.jacobian = FALSE,
  DoF.max = min(ncol(X) + 1, nrow(X) - 1)
)

Arguments

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).
compute.jacobian: Should the first derivative of the regression coefficients be computed as well? Default is FALSE
DoF.max: upper bound on the Degrees of Freedom. Default is min(ncol(X)+1,nrow(X)-1).

Value

coefficients: matrix of regression coefficients
intercept: vector of regression intercepts
DoF: Degrees of Freedom
sigmahat: vector of estimated model error
Yhat: matrix of fitted values
yhat: vector of squared length of fitted values
RSS: vector of residual sum of error
covariance: NULL object.
TT: matrix of normalized PLS components

Details

We first standardize X to zero mean and unit variance.

References

Kraemer, N., Sugiyama M. (2011). "The Degrees of Freedom of Partial Least Squares Regression". Journal of the American Statistical Association 106 (494) https://www.tandfonline.com/doi/abs/10.1198/jasa.2011.tm10107

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

Author

Nicole Kraemer, Mikio L. Braun

Examples


n<-50 # number of observations
p<-5 # number of variables
X<-matrix(rnorm(n*p),ncol=p)
y<-rnorm(n)


pls.object<-kernel.pls.fit(X,y,m=5,compute.jacobian=TRUE)