demu (version 0.3.0)

sim.dpp.modal.nystrom: Draw samples from the conditional DPP design emulator using grid-based Nystrom approximation.

Description

sim.dpp.modal.nystrom() uses the DPP-based design emulator of Pratola et al. (2018) to draw a sample of the n-run optimal design for a Gaussian process regression model with stationary correlation function \(r(x,x^\prime)\), where the entries of R are formed by evaluating \(r(x,x^\prime)\) over a grid of candidate locations. This function uses a grid-based Nystrom approximation based on the passed matrix X to avoid constructing a large correlation matrix if dimension ngrid^p and its subsequent eigendecomposition.

Usage

sim.dpp.modal.nystrom(Xin,rho,n=0,ngrid=NULL,method="Nystrom")

Arguments

Xin

A initial \(n\times p\) matrix of points.

rho

The \(p\times 1\) parameter vector for the Gaussian correlation model.

n

Size of the design to sample from the candidate grid.

ngrid

Size of the candidate grid will be ngrid^p.

method

Type of approximation to use. Currently only supports ``Nystrom''.

Value

A list containing the candidate points constructed and the points selected as the design sites from this candidate set as well as their indices.

Details

For more details on the method, see Pratola et al. (2018). Detailed examples demonstrating the method are available at http://www.matthewpratola.com/software.

References

Pratola, Matthew T., Lin, C. Devon, and Craigmile, Peter. (2018) Optimal Design Emulators: A Point Process Approach. arXiv:1804.02089.

See Also

demu-package sim.dpp.modal sim.dpp.modal.nystrom.kmeans

Examples

# NOT RUN {
library(demu)

# Starting design
X=matrix(runif(10*2),ncol=2)
rho=rep(0.01,2)
n=10
ngrid=11
samp=sim.dpp.modal.nystrom(X,rho,n,ngrid)
samp$design

# Could plot the result:
# plot(samp$X,xlim=c(0,1),ylim=c(0,1))
# points(samp$X[samp$pts,],pch=20)
# }