Package 'TAG' reference manual

Title:	Transformed Additive Gaussian Processes
Description:	Implement the transformed additive Gaussian (TAG) process and the transformed approximately additive Gaussian (TAAG) process proposed in Lin and Joseph (2020) <DOI:10.1080/00401706.2019.1665592>. These functions can be used to model deterministic computer experiments, obtain predictions at new inputs, and quantify the uncertainty of the predictions. This research is supported by a U.S. National Science Foundation grant DMS-1712642 and a U.S. Army Research Office grant W911NF-17-1-0007.
Authors:	Li-Hsiang Lin and V. Roshan Joseph
Maintainer:	Li-Hsiang Lin <[email protected]>
License:	GPL-2
Version:	0.5.1
Built:	2024-11-13 05:15:02 UTC
Source:	https://github.com/cran/TAG

Check TAAG

Description

This function provides a table for checking whther the TAAG process fits the data well better than an ordinary kriging model.

Usage

check.TAAG(object)
check.TAAG(object)

Arguments

object

object of class inheriting from "TAAG".

Value

A table of the fitted negative likelihood values and cross validation errors obtained from TAAG and the ordinary kriging models from dicekriging and mlegp is returned. Note that, for both criteria, the model with a smaller value are a better model.

References

Lin, L.-H. and Joseph, V. R. (2020) "Transformation and Additivity in Gaussian Processes",Technometrics, 62, 525-535. DOI:10.1080/00401706.2019.1665592.

Examples

n <- 20
p <- 2
library(randtoolbox)
X <-  sobol(n, dim = p, init = TRUE, scrambling = 2, seed = 20, normal = FALSE)
y <- exp(2*sin(0.5*pi*X[,1]) + 0.5*cos(2.5*pi*X[,2]))
ini.TAG <- initial.TAG(y, X)
par.TAG <- TAG(ini.TAG)
N <- 1000
X.test <- sobol(N, dim = p, init = TRUE, scrambling = 2, seed = 5, normal = FALSE)
ytrue  <- exp(2*sin(0.5*pi*X.test[,1]) + 0.5*cos(2.5*pi*X.test[,2]))
pre.TAG <- pred.TAG(par.TAG, X.test)
library(DiceKriging)
set.seed(2)
temp.m <- km(formula=~1, design=X, response=par.TAG$ty,
             covtype="gauss",nugget = (10^-15), multistart = 4,
             control = list(trace = FALSE))
nu.est <- sqrt(2*(coef(temp.m)$range^2))
par.TAAG <- TAAG(par.TAG, nu.est)

check.table <- check.TAAG(par.TAAG)
check.table
n <- 20
p <- 2
library(randtoolbox)
X <-  sobol(n, dim = p, init = TRUE, scrambling = 2, seed = 20, normal = FALSE)
y <- exp(2*sin(0.5*pi*X[,1]) + 0.5*cos(2.5*pi*X[,2]))
ini.TAG <- initial.TAG(y, X)
par.TAG <- TAG(ini.TAG)
N <- 1000
X.test <- sobol(N, dim = p, init = TRUE, scrambling = 2, seed = 5, normal = FALSE)
ytrue  <- exp(2*sin(0.5*pi*X.test[,1]) + 0.5*cos(2.5*pi*X.test[,2]))
pre.TAG <- pred.TAG(par.TAG, X.test)
library(DiceKriging)
set.seed(2)
temp.m <- km(formula=~1, design=X, response=par.TAG$ty,
             covtype="gauss",nugget = (10^-15), multistart = 4,
             control = list(trace = FALSE))
nu.est <- sqrt(2*(coef(temp.m)$range^2))
par.TAAG <- TAAG(par.TAG, nu.est)

check.table <- check.TAAG(par.TAAG)
check.table

Leave-One-Out Cross Validation Error of a TAG or TAAG Process

Description

This function evaluates the leave-one-out cross validation errors of a TAG or TAAG process.

Usage

cv.TAAG(object, TAAG.indicator  = FALSE)
cv.TAAG(object, TAAG.indicator  = FALSE)

Arguments

`object`	object of class inheriting from "TAG" or "TAAG".
`TAAG.indicator`	logical. If TRUE, the object is from TAAG; otherwise, from TAG.

Value

The values returned from the function is a list containing:

`CV`	Leave-one-out cross validation errors in the original scale of y.
`TCV`	Leave-one-out cross validation errors in the transformed scale.

References

Lin, L.-H. and Joseph, V. R. (2020) "Transformation and Additivity in Gaussian Processes",Technometrics, 62, 525-535. DOI:10.1080/00401706.2019.1665592.

Examples

n <- 20
p <- 2
library(randtoolbox)
X <- sobol(n, dim = p, init = TRUE, scrambling = 2, seed = 20, normal = FALSE)
y <- exp(2*sin(0.5*pi*X[,1]) + 0.5*cos(2.5*pi*X[,2]))
ini.TAG <- initial.TAG(y, X)
par.TAG <- TAG(ini.TAG)
cv.scores <- cv.TAAG(par.TAG)
(CV.TAG <- cv.scores$CV)
(TCV.TAG <- cv.scores$TCV)
n <- 20
p <- 2
library(randtoolbox)
X <- sobol(n, dim = p, init = TRUE, scrambling = 2, seed = 20, normal = FALSE)
y <- exp(2*sin(0.5*pi*X[,1]) + 0.5*cos(2.5*pi*X[,2]))
ini.TAG <- initial.TAG(y, X)
par.TAG <- TAG(ini.TAG)
cv.scores <- cv.TAAG(par.TAG)
(CV.TAG <- cv.scores$CV)
(TCV.TAG <- cv.scores$TCV)

Initial Values of TAG Process

Description

This function generates good initial values for the parameters in a TAG process.

Usage

initial.TAG(y, X, Candi.lambda = seq(from=-2, to=2,by=0.5),
            Adj.omega = TRUE, nug=0.001, nbasis=10, rannum=20, big=FALSE, nsub=31,
            method.1d = "DiceKriging")
initial.TAG(y, X, Candi.lambda = seq(from=-2, to=2,by=0.5),
            Adj.omega = TRUE, nug=0.001, nbasis=10, rannum=20, big=FALSE, nsub=31,
            method.1d = "DiceKriging")

Arguments

`y`	a response vector of size n, where n is the sample size.
`X`	an n by p design matrix, where n is the sample size, and p is the number of input variables.
`Candi.lambda`	a vector containing the candidate values of the Box-Cox transformation parameter. Default is seq(from=-2, to=2,by=0.5).
`Adj.omega`	logical. If TRUE, the initial estimates for weight parameters are adjusted to avoid 0. Default is TRUE.
`nug`	a nonnegative value used as the nugget term for fitting the 1-dim GP models. Default is 0.001.
`nbasis`	a positive integer specifying the basis dimension used in mgcv. Default is 10.
`rannum`	a positive integer specifying the number of starting values in DiceKriging. Default is 2.
`big`	logical. If TRUE, the bam function in the mgcv package is used; otherwise, the gam function is used. Default is FALSE.
`nsub`	a positive integer specifying the number of design points used for obtaining the initial estimates of the length scale parameters. Default is 31.
`method.1d`	the method used for fitting the 1-dimensional GPs. Currently, the method can be DiceKriging or mlegp.

Value

The values returned from the function is a list containing the following components:

`omega`	The initial estimates of the weight parameters.
`s`	The initial estimates of the length scale parameters.
`lambda`	The initial estimate of the Box-Cox transformation parameter.
`delta`	The initial estimate of the nugget parameter.
`nbases`	The number of bases used in each dimension.
`y`	The response vector.
`X`	The n by p input design matrix.

References

Lin, L.-H. and Joseph, V. R. (2020) "Transformation and Additivity in Gaussian Processes",Technometrics, 62, 525-535. DOI:10.1080/00401706.2019.1665592.

Olivier Roustant, David Ginsbourger, Yves Deville (2012). DiceKriging, DiceOptim: Two R Packages for the Analysis of Computer Experiments by Kriging-Based Metamodeling and Optimization. Journal of Statistical Software, 51, 1-55.

Dancik, GM and Dorman, KS (2008). mlegp: Statistical analysis for computer models of biological systems using R. Bioinformatics 24, 1966-1967

Wood, S.N. (2017) Generalized Additive Models: An Introduction with R (2nd edition). New York: CRC press.

Examples

n <- 20
p <- 2
library(randtoolbox)
X <-  sobol(n, dim = p, init = TRUE, scrambling = 2, seed = 20, normal = FALSE)
y <- exp(2*sin(0.5*pi*X[,1]) + 0.5*cos(2.5*pi*X[,2]))
ini.TAG <- initial.TAG(y, X)


#An example for some inputs with fewer levels
n <- 18
p <- 2
X1 <- rep(c(0,1,2)/3, 6) # A factor with fewer levels
library(randtoolbox)
X2 <-  sobol(n, dim = 1, init = TRUE, scrambling = 2, seed = 20, normal = FALSE)
X <- cbind(X1, X2)
y <- exp(2*sin(0.5*pi*X[,1]) + 0.5*cos(2.5*pi*X[,2]))
ini.TAG <- initial.TAG(y, X)
n <- 20
p <- 2
library(randtoolbox)
X <-  sobol(n, dim = p, init = TRUE, scrambling = 2, seed = 20, normal = FALSE)
y <- exp(2*sin(0.5*pi*X[,1]) + 0.5*cos(2.5*pi*X[,2]))
ini.TAG <- initial.TAG(y, X)


#An example for some inputs with fewer levels
n <- 18
p <- 2
X1 <- rep(c(0,1,2)/3, 6) # A factor with fewer levels
library(randtoolbox)
X2 <-  sobol(n, dim = 1, init = TRUE, scrambling = 2, seed = 20, normal = FALSE)
X <- cbind(X1, X2)
y <- exp(2*sin(0.5*pi*X[,1]) + 0.5*cos(2.5*pi*X[,2]))
ini.TAG <- initial.TAG(y, X)

Main Effects Plots from a TAG Process

Description

This function produces the main effects plot from a TAG process.

Usage

plotTAG(object, include.legend = TRUE, legend.position = "bottomright")
plotTAG(object, include.legend = TRUE, legend.position = "bottomright")

Arguments

`object`	object of class inheriting from "TAG".
`include.legend`	logical value indicating if the legend of the main effects plot is required.
`legend.position`	a character indicating the position of the legend.

Details

The location of the legend is "bottomright", "bottom", "bottomleft", "left", "topleft", "top", "topright", "right", or "center".

Value

A main effects plot in the transformed scale of the response is returned.

References

Lin, L.-H. and Joseph, V. R. (2020) "Transformation and Additivity in Gaussian Processes",Technometrics, 62, 525-535. DOI:10.1080/00401706.2019.1665592.

Examples

n <- 20
p <- 2
library(randtoolbox)
X <-  sobol(n, dim = p, init = TRUE, scrambling = 2, seed = 20, normal = FALSE)
y <- exp(2*sin(0.5*pi*X[,1]) + 0.5*cos(2.5*pi*X[,2]))
ini.TAG <- initial.TAG(y, X)
par.TAG <- TAG(ini.TAG)
plotTAG(par.TAG)
n <- 20
p <- 2
library(randtoolbox)
X <-  sobol(n, dim = p, init = TRUE, scrambling = 2, seed = 20, normal = FALSE)
y <- exp(2*sin(0.5*pi*X[,1]) + 0.5*cos(2.5*pi*X[,2]))
ini.TAG <- initial.TAG(y, X)
par.TAG <- TAG(ini.TAG)
plotTAG(par.TAG)

Prediction from the TAAG Process

Description

This function provides predictions from a TAAG process.

Usage

pred.TAAG(object, newX, predict.CI = FALSE,  zalpha = 1.96)
pred.TAAG(object, newX, predict.CI = FALSE,  zalpha = 1.96)

Arguments

`object`	object of class inheriting from "TAAG".
`newX`	matrix of new values of x at which predictions are needed.
`predict.CI`	logical value indicating if the confidence interval at each prediction point is required.
`zalpha`	normal critical value for the confidence interval. Default is 1.96 for 95 % confidence intervals. The zalpha works only when predict.CI is TRUE.

Value

The function returns predictions at newX and the confidence intervals (if predict.CI is TRUE). If predict.CI is TRUE, the values returned from the function is a list containing:

`Prediction`	the prediction at newX.
`ConfidenceLB`	the lower bound of the prediction confidence interval at newX.(Note that the default is 95 %.)
`ConfidenceUB`	the upper bound of the prediction confidence interval at newX.

References

Lin, L.-H. and Joseph, V. R. (2020) "Transformation and Additivity in Gaussian Processes",Technometrics, 62, 525-535. DOI:10.1080/00401706.2019.1665592.

Examples

n <- 20
p <- 2
library(randtoolbox)
X <-   sobol(n, dim = p, init = TRUE, scrambling = 2, seed = 20, normal = FALSE)
y <- exp(2*sin(0.5*pi*X[,1]) + 0.5*cos(2.5*pi*X[,2]))
ini.TAG <- initial.TAG(y, X)
par.TAG <- TAG(ini.TAG)
N <- 1000 # size of testing samples
X.test <-  sobol(N, dim = p, init = TRUE, scrambling = 2, seed = 5, normal = FALSE)
ytrue  <- exp(2*sin(0.5*pi*X.test[,1]) + 0.5*cos(2.5*pi*X.test[,2]))
pre.TAG <- pred.TAG(par.TAG, X.test)
library(DiceKriging)
set.seed(2)
temp.m <- km(formula=~1, design=X, response=par.TAG$ty,
   covtype="gauss",nugget = (10^-15), multistart = 4,
   control = list(trace = FALSE, verbose = FALSE))
nu.est <- sqrt(2*(coef(temp.m)$range^2))
par.TAAG <- TAAG(par.TAG, nu.est)
pre.TAAG <- pred.TAAG(par.TAAG, X.test)
mean((pre.TAAG$Prediction-ytrue)^2)
n <- 20
p <- 2
library(randtoolbox)
X <-   sobol(n, dim = p, init = TRUE, scrambling = 2, seed = 20, normal = FALSE)
y <- exp(2*sin(0.5*pi*X[,1]) + 0.5*cos(2.5*pi*X[,2]))
ini.TAG <- initial.TAG(y, X)
par.TAG <- TAG(ini.TAG)
N <- 1000 # size of testing samples
X.test <-  sobol(N, dim = p, init = TRUE, scrambling = 2, seed = 5, normal = FALSE)
ytrue  <- exp(2*sin(0.5*pi*X.test[,1]) + 0.5*cos(2.5*pi*X.test[,2]))
pre.TAG <- pred.TAG(par.TAG, X.test)
library(DiceKriging)
set.seed(2)
temp.m <- km(formula=~1, design=X, response=par.TAG$ty,
   covtype="gauss",nugget = (10^-15), multistart = 4,
   control = list(trace = FALSE, verbose = FALSE))
nu.est <- sqrt(2*(coef(temp.m)$range^2))
par.TAAG <- TAAG(par.TAG, nu.est)
pre.TAAG <- pred.TAAG(par.TAAG, X.test)
mean((pre.TAAG$Prediction-ytrue)^2)

Prediction from the TAG process

Description

This function provides predictions from a TAG process.

Usage

pred.TAG(object, newX)
pred.TAG(object, newX)

Arguments

`object`	object of class inheriting from "TAG".
`newX`	matrix of new x values at which predictions are needed.

Value

The values returned from the function are the predictions at newX.

References

Lin, L.-H. and Joseph, V. R. (2020) "Transformation and Additivity in Gaussian Processes",Technometrics, 62, 525-535. DOI:10.1080/00401706.2019.1665592.

Examples

n <- 20
p <- 2
library(randtoolbox)
X <-  sobol(n, dim = p, init = TRUE, scrambling = 2, seed = 20, normal = FALSE)
y <- exp(2*sin(0.5*pi*X[,1]) + 0.5*cos(2.5*pi*X[,2]))
ini.TAG <- initial.TAG(y, X)
par.TAG <- TAG(ini.TAG)
N <- 1000
X.test <- sobol(N, dim = p, init = TRUE, scrambling = 2, seed = 5, normal = FALSE)
ytrue  <- exp(2*sin(0.5*pi*X.test[,1]) + 0.5*cos(2.5*pi*X.test[,2]))
pre.TAG <- pred.TAG(par.TAG, X.test)
n <- 20
p <- 2
library(randtoolbox)
X <-  sobol(n, dim = p, init = TRUE, scrambling = 2, seed = 20, normal = FALSE)
y <- exp(2*sin(0.5*pi*X[,1]) + 0.5*cos(2.5*pi*X[,2]))
ini.TAG <- initial.TAG(y, X)
par.TAG <- TAG(ini.TAG)
N <- 1000
X.test <- sobol(N, dim = p, init = TRUE, scrambling = 2, seed = 5, normal = FALSE)
ytrue  <- exp(2*sin(0.5*pi*X.test[,1]) + 0.5*cos(2.5*pi*X.test[,2]))
pre.TAG <- pred.TAG(par.TAG, X.test)

Transformed Approximately Additive Gaussian Process

Description

This function fits the Transformed Approximately Additive Gaussian (TAAG) process.

Usage

TAAG(parTAG, nu.est, adj.nu = FALSE)
TAAG(parTAG, nu.est, adj.nu = FALSE)

Arguments

`parTAG`	object of class inheriting from "TAG".
`nu.est`	the estimates of the length scale parameters from a standard GP.
`adj.nu`	logical. If FALSE, the proportional parameter $\eta$ is estimated; otherwise, both $\eta$ and the multiplication factor $\phi$ are estimated. Default is FALSE.

Details

The details of TAAG process can be found in Lin and Joseph (2019).

When the input dimension is high, set adj.nu = TRUE and nu.est = s0, where s0 is the initial values of the length scale parameters from the function initial.TAG. Then, the length scale parameter $\nu$ is set to $\phi \times$ s0, and $\phi$ is estimated through function TAAG.. This is useful especially when the input dimension is high.

Value

The values returned from the function is a list containing the following components:

`omega`	The estimates of the weight parameters.
`s`	The estimates of the length scale parameters.
`nu`	The estimates of the length scale parameter $\nu$ .
`lambda`	The estimate of the Box-Cox transformation parameter.
`eta`	The estimate of the proportion parameter.
`phi`	The estimate of the multiplication factor for $\nu$ , used for high dimensional data.
`obj.fun`	The negative of log-unnormalized posterior value (value of the objective function)
`ty`	The transformed response vector.
`X`	The n by p input design matrix.

References

Lin, L.-H. and Joseph, V. R. (2020) "Transformation and Additivity in Gaussian Processes",Technometrics, 62, 525-535. DOI:10.1080/00401706.2019.1665592.

Examples

n <- 20
p <- 2
library(randtoolbox)
X <-  sobol(n, dim = p, init = TRUE, scrambling = 2, seed = 20, normal = FALSE)
y <- exp(2*sin(0.5*pi*X[,1]) + 0.5*cos(2.5*pi*X[,2]))
ini.TAG <- initial.TAG(y, X)
par.TAG <- TAG(ini.TAG)
N <- 1000
X.test <- sobol(N, dim = p, init = TRUE, scrambling = 2, seed = 5, normal = FALSE)
ytrue  <- exp(2*sin(0.5*pi*X.test[,1]) + 0.5*cos(2.5*pi*X.test[,2]))
pre.TAG <- pred.TAG(par.TAG, X.test)
library(DiceKriging)
set.seed(2)
temp.m <- km(formula=~1, design=X, response=par.TAG$ty,
             covtype="gauss",nugget = (10^-15), multistart = 4,
             control = list(trace = FALSE, verbose = FALSE))
nu.est <- sqrt(2*(coef(temp.m)$range^2))
par.TAAG <- TAAG(par.TAG, nu.est)
n <- 20
p <- 2
library(randtoolbox)
X <-  sobol(n, dim = p, init = TRUE, scrambling = 2, seed = 20, normal = FALSE)
y <- exp(2*sin(0.5*pi*X[,1]) + 0.5*cos(2.5*pi*X[,2]))
ini.TAG <- initial.TAG(y, X)
par.TAG <- TAG(ini.TAG)
N <- 1000
X.test <- sobol(N, dim = p, init = TRUE, scrambling = 2, seed = 5, normal = FALSE)
ytrue  <- exp(2*sin(0.5*pi*X.test[,1]) + 0.5*cos(2.5*pi*X.test[,2]))
pre.TAG <- pred.TAG(par.TAG, X.test)
library(DiceKriging)
set.seed(2)
temp.m <- km(formula=~1, design=X, response=par.TAG$ty,
             covtype="gauss",nugget = (10^-15), multistart = 4,
             control = list(trace = FALSE, verbose = FALSE))
nu.est <- sqrt(2*(coef(temp.m)$range^2))
par.TAAG <- TAAG(par.TAG, nu.est)

Transformed Additive Gaussian Process

Description

This function fits the Transformed Additive Gaussian (TAG) process.

Usage

TAG(iniTAG, HighD = FALSE, delta.threshold = -6)
TAG(iniTAG, HighD = FALSE, delta.threshold = -6)

Arguments

`iniTAG`	object of class inheriting from "initial.TAG".
`HighD`	logical. If TRUE, only $\kappa$ and delta will be estimated. This is useful for high dimensional data. Default is False.
`delta.threshold`	the minimum value of log10(delta). Default is -6.

Details

The details of the TAG process can be found in Lin and Joseph (2019).

When HighD = FALSE, the weight parameters, the length scale parameters, the nugget parameter, and the Box-Cox transformation parameter are estimated. When HighD = TRUE, the length scale parameters for TAG is $\eta$ *s0, where s0 is the initial estimate of the length scale parameters. Only $\eta$ and the nugget parameter are estimated.

Value

The values returned from the function is a list containing the following components:

`omega`	The estimates of the weight parameters.
`s`	The estimates of the length scale parameters.
`lambda`	The estimate of the Box-Cox transformation parameter.
`delta`	The estimate of the nugget parameter in log10 scale. For example, delta $= -6$ means that the estimate of the nugget is $10^(-6)$ .
`kappa`	If HighD is true, an estimate of kappa will be returned, which is a multiplication factor for the initial estimates of the length scale parameters.
`ty`	The transformed response vector.
`X`	The n by p input design matrix.

References

Lin, L.-H. and Joseph, V. R. (2020) "Transformation and Additivity in Gaussian Processes",Technometrics, 62, 525-535. DOI:10.1080/00401706.2019.1665592.

Examples

n <- 20
p <- 2
library(randtoolbox)
X <-  sobol(n, dim = p, init = TRUE, scrambling = 2, seed = 20, normal = FALSE)
y <- exp(2*sin(0.5*pi*X[,1]) + 0.5*cos(2.5*pi*X[,2]))
ini.TAG <- initial.TAG(y, X)
par.TAG <- TAG(ini.TAG)
n <- 20
p <- 2
library(randtoolbox)
X <-  sobol(n, dim = p, init = TRUE, scrambling = 2, seed = 20, normal = FALSE)
y <- exp(2*sin(0.5*pi*X[,1]) + 0.5*cos(2.5*pi*X[,2]))
ini.TAG <- initial.TAG(y, X)
par.TAG <- TAG(ini.TAG)

Conducting All Steps for Building TAG Processes

Description

This function combines functions initial.TAG, TAG, and TAAG together, so it generates the estimated parameters from a completed TAG process. The returned object from TAG1step is in the same format as the one returned from TAAG, so the returned object can be passed to function pred.TAAG for predictions.

Usage

TAG1step(y, X,
         set.initial = list(Candi.lambda= seq(from=-2, to=2,by=0.5)),
         set.TAG = list(delta.threshold = -6),
         set.TAAG = list(adj.nu = FALSE))
TAG1step(y, X,
         set.initial = list(Candi.lambda= seq(from=-2, to=2,by=0.5)),
         set.TAG = list(delta.threshold = -6),
         set.TAAG = list(adj.nu = FALSE))

Arguments

`y`	a response vector of size n, where n is the sample size.
`X`	an n by p design matrix, where n is the sample size, and p is the number of input variables.
`set.initial`	a list for controling other arguments in function Initial.TAG. See Initial.TAG for more detials.
`set.TAG`	a list for controling other arguments in function TAG. See TAG for more detials.
`set.TAAG`	a list for controling other arguments in function TAAG. See TAAG for more detials.

Value

The values returned from the function is a list containing the following components:

`omega`	The estimates of the weight parameters.
`s`	The estimates of the length scale parameters.
`nu`	The estimates of the length scale parameter $\nu$ .
`lambda`	The estimate of the Box-Cox transformation parameter.
`eta`	The estimate of the proportion parameter.
`phi`	The estimate of the multiplication factor for $\nu$ , used for high dimensional data.
`obj.fun`	The negative of log-unnormalized posterior value (value of the objective function)
`ty`	The transformed response vector.
`X`	The n by p input design matrix.

References

Lin, L.-H. and Joseph, V. R. (2020) "Transformation and Additivity in Gaussian Processes",Technometrics, 62, 525-535. DOI:10.1080/00401706.2019.1665592.

Dancik, GM and Dorman, KS (2008). mlegp: Statistical analysis for computer models of biological systems using R. Bioinformatics 24, 1966-1967

Wood, S.N. (2017) Generalized Additive Models: An Introduction with R (2nd edition). New York: CRC press.

Examples

n <- 20
p <- 2
library(randtoolbox)
X <-  sobol(n, dim = p, init = TRUE, scrambling = 2, seed = 20, normal = FALSE)
y <- exp(2*sin(0.5*pi*X[,1]) + 0.5*cos(2.5*pi*X[,2]))
par.TAAG <- TAG1step(y, X)

#Predictions From TAG1step
N <- 1000 # size of testing samples
X.test <-  sobol(N, dim = p, init = TRUE, scrambling = 2, seed = 5, normal = FALSE)
ytrue  <- exp(2*sin(0.5*pi*X.test[,1]) + 0.5*cos(2.5*pi*X.test[,2]))
pre.TAAG <- pred.TAAG(par.TAAG, X.test)
mean((pre.TAAG$Prediction-ytrue)^2)
n <- 20
p <- 2
library(randtoolbox)
X <-  sobol(n, dim = p, init = TRUE, scrambling = 2, seed = 20, normal = FALSE)
y <- exp(2*sin(0.5*pi*X[,1]) + 0.5*cos(2.5*pi*X[,2]))
par.TAAG <- TAG1step(y, X)

#Predictions From TAG1step
N <- 1000 # size of testing samples
X.test <-  sobol(N, dim = p, init = TRUE, scrambling = 2, seed = 5, normal = FALSE)
ytrue  <- exp(2*sin(0.5*pi*X.test[,1]) + 0.5*cos(2.5*pi*X.test[,2]))
pre.TAAG <- pred.TAAG(par.TAAG, X.test)
mean((pre.TAAG$Prediction-ytrue)^2)

Package 'TAG'

Help Index

Check TAAG

Description

Usage

Arguments

Value

References

See Also

Examples

Leave-One-Out Cross Validation Error of a TAG or TAAG Process

Description

Usage

Arguments

Value

References

See Also

Examples

Initial Values of TAG Process

Description

Usage

Arguments

Value

References

Examples

Main Effects Plots from a TAG Process

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Prediction from the TAAG Process

Description

Usage

Arguments

Value

References

See Also

Examples

Prediction from the TAG process

Description

Usage

Arguments

Value

References

See Also

Examples

Transformed Approximately Additive Gaussian Process

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Transformed Additive Gaussian Process

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Conducting All Steps for Building TAG Processes

Description

Usage

Arguments

Value

References

See Also

Examples