TAAG: Transformed Approximately Additive Gaussian Process

In TAG: Transformed Additive Gaussian Processes

Description

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

Usage

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 η is estimated; otherwise, both η and the multiplication factor φ 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 ν is set to φ \times s0, and φ 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 ν.
lambda	The estimate of the Box-Cox transformation parameter.
eta	The estimate of the proportion parameter.
phi	The estimate of the multiplication factor for ν, 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.

See Also

TAG for the estimates of the TAG parameters, and pred.TAAG for predictions.

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)

TAG documentation built on June 8, 2021, 1:06 a.m.