DiceEval-package {DiceEval}R Documentation

Metamodels

Description

Construction and evaluation of metamodels.

Package: DiceEval
Type: Package
Version: 1.4
Date: 2015-06-15
License: GPL-3

Details

This package is dedicated to the construction of metamodels. A validation procedure is also proposed using usual criteria (RMSE, MAE etc.) and cross-validation procedure. Moreover, graphical tools help to choose the best value for the penalty parameter of a stepwise or a PolyMARS model. Another routine is dedicated to the comparison of metamodels.

Note

This work was conducted within the frame of the DICE (Deep Inside Computer Experiments) Consortium between ARMINES, Renault, EDF, IRSN, ONERA and TOTAL S.A. (http://emse.dice.fr/).

Functions gam, mars and polymars are required for the construction of metamodels. km provides Kriging models.

Author(s)

D. Dupuy & C. Helbert

References

Dupuy D., Helbert C., Franco J. (2015), DiceDesign and DiceEval: Two R-Packages for Design and Analysis of Computer Experiments, Journal of Statistical Software, 65(11), 1–38, http://www.jstatsoft.org/v65/i11/.

Friedman J. (1991), Multivariate Adaptative Regression Splines (invited paper), Annals of Statistics, 10/1, 1-141.

Hastie T. and Tibshirani R. (1990), Generalized Additive Models, Chapman and Hall, London.

Hastie T., Tibshirani R. and Friedman J. (2001), The Elements of Statistical Learning : Data Mining, Inference and Prediction, Springer.

Helbert C. and Dupuy D. (2007-09-26), Retour d'exp?riences sur m?tamod?les : partie th?orique, Livrable r?dig? dans le cadre du Consortium DICE.

Kooperberg C., Bose S. and Stone C.J. (1997), Polychotomous Regression, Journal of the American Statistical Association, 92 Issue 437, 117-127.

Rasmussen C.E. and Williams C.K.I. (2006), Gaussian Processes for Machine Learning, the MIT Press, www.GaussianProcess.org/gpml.

Stones C., Hansen M.H., Kooperberg C. and Truong Y.K. (1997), Polynomial Splines and their Tensor Products in Extended Linear Modeling, Annals of Statistics, 25/4, 1371-1470.

See Also

modelFit, modelPredict, crossValidation and modelComparison

Different space-filling designs can be found in the DiceDesign package and we refer to the DiceKriging package for the construction of kriging models. This package takes part of a toolbox inplemented during the Dice consortium.

Examples

## Not run: 
rm(list=ls())
# A 2D example
Branin	<- function(x1,x2) {
x1	<- 1/2*(15*x1+5)   
x2	<- 15/2*(x2+1)
(x2 - 5.1/(4*pi^2)*(x1^2) + 5/pi*x1 - 6)^2 + 10*(1 - 1/(8*pi))*cos(x1) + 10
}
# A 2D uniform design with n points in [-1,1]^2
n	<- 50
X	<- matrix(runif(n*2,-1,1),ncol=2,nrow=n)
Y	<- Branin(X[,1],X[,2])
Z	<- (Y-mean(Y))/sd(Y)

# Construction of a PolyMARS model with a penalty parameter equal to 2
library(polspline)
modPolyMARS	<- modelFit(X,Z,type = "PolyMARS",gcv=2.2)

# Prediction and comparison between the exact function and the predicted one
xtest	<- seq(-1, 1, length= 21) 
ytest	<- seq(-1, 1, length= 21)
Zreal	<- outer(xtest, ytest, Branin)
Zreal	<- (Zreal-mean(Y))/sd(Y)
Zpredict	<- modelPredict(modPolyMARS,expand.grid(xtest,ytest))
m	<- min(floor(Zreal),floor(Zpredict))
M	<- max(ceiling(Zreal),ceiling(Zpredict))
persp(xtest, ytest, Zreal, theta = 30, phi = 30, expand = 0.5,
	col = "lightblue",main="Branin function",zlim=c(m,M),
	ticktype = "detailed")

persp(xtest, ytest, matrix(Zpredict,nrow=length(xtest),
	ncol=length(ytest)), theta = 30, phi = 30, expand = 0.5,
	col = "lightblue",main="PolyMARS Model",zlab="Ypredict",zlim=c(m,M),
	ticktype = "detailed")

# Comparison of models
modelComparison(X,Y,type=c("Linear", "StepLinear","PolyMARS","Kriging"),
	formula=Y~X1+X2+X1:X2+I(X1^2)+I(X2^2),penalty=log(dim(X)[1]), gcv=4)

# see also the demonstration example in dimension 5 (source: IRSN)
demo(IRSN5D)

## End(Not run)

[Package DiceEval version 1.5 Index]