qnormscale: Scaling of Inducing Point Design based on Inverse Gaussian...
In liGP: Locally Induced Gaussian Process Regression

Description Usage Arguments Details Value Author(s) References See Also Examples

Scales a set of proposed inducing point locations in [0,1]^d to center around a reference location, returning the scaled design

1	qnormscale(X, mean, sd)

`X`	a `matrix` or containing a proposed inducing point design in [0,1]^d
`mean`	a vector representing the reference location to act as the center of the scaling; `length(mean) = ncol(X)`
`sd`	a scalar or vector determining the standard deviation for each dimension of the Gaussian CDF

This function scales a set of proposed inducing points in [0,1]^d to be centered and concentrated around a reference location. The proposed inducing points are interpreted as quantiles of one-dimensional Gaussian distributions centered at the reference location with the standard deviation provided by the user. For each dimension qnorm is invoked to rescale the inducing points.

a matrix of the scaled set of inducing points

D. Austin Cole austin.cole8@vt.edu

D.A. Cole, R.B. Christianson, and R.B. Gramacy (2021). Locally Induced Gaussian Processes for Large-Scale Simulation Experiments Statistics and Computing, 31(3), 1-21; preprint on arXiv:2008.12857; https://arxiv.org/abs/2008.12857

qnorm

## Generate data and define xmean
X <- matrix(runif(30), ncol=2)
xmean <- c(0.3, 0.4) # doesn't need to be in [0,1]^2

## Scale centered at xmean with different standard deviations
X_scaled1 <- qnormscale(X, mean=xmean, sd=.1)
X_scaled2 <- qnormscale(X, mean=xmean, sd=c(.05,.15))

## View scaled X
plot(X, xlab='X1', ylab='X2')
points(xmean[1], xmean[2], pch=16)
points(X_scaled1, pch=2, col=3, lwd=2)
points(X_scaled2, pch=3, col=4, lwd=2)
legend('topright',legend = c('Original X','xmean', 'Xscaled1', 'Xscaled2'),
       pch = c(1,16,2,3), col= c(1,1,3,4), lwd=2, lty=NA)