sim.dpp.modal.np {demu}

Draw samples from the conditional DPP design emulator using a kmeans-based Nystrom approximation.

Description

sim.dpp.modal.np() uses sim.dpp.modal.nystrom.kmeans() to draw a design of n points in p dimensions using the kmeans-based Nystrom approximation of Zhang and Kwok (2010) and the DPP-based design emulator of Pratola et al. (2018). The design constructed assumes 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 set of landmarks chosen by the kmeans algorithm, and the resulting eigenvectors are projected into the higher dimensional space using the Nystrom approximation. Additional options for sim.dpp.modal.nystrom.kmeans() can be passed to alter the construction of the landmark set.

Usage

sim.dpp.modal.np(n,p,N,rho,m=max(ceiling(N*0.1),n),...)

Arguments

n

Size of the desired design.

p

Dimension of the desired design.

N

Number of kernel approximation points drawn uniformly from the p-dimensional design space.

rho

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

m

Number of landmark points to use in constructing the kmeans-based Nystrom approximation.

...

Additional options to pass to sim.dpp.modal.nystrom.kmeans() for drawing the design.

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.

Value

A list containing a matrix which is the union of the N\times p uniformly sampled kernel approximation points and the m selected landmark sites, and the indices into this matrix of the selected design sites.

References

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

Zhang, Kai and Kwok, James T. (2010) Clustered Nystrom method for large scale manifold learning and dimension reduction. IEEE Transactions on Neural Networks, 21.10, 1576–1587. doi: 10.1109/TNN.2010.2064786

See Also

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

Examples

library(demu)

n=50
p=5
N=500
rho=rep(0.01,5)
samp=sim.dpp.modal.np(n,p,N,rho)

# Could plot the result:
# pchvec=rep(1,nrow(samp$X))
# pchvec[samp$pts]=20
# cexvec=rep(0.1,nrow(samp$X))
# cexvec[samp$pts]=1
# colvec=rep("black",nrow(samp$X))
# colvec[samp$pts]="red"
# pairs(samp$X,pch=pchvec,cex=cexvec,col=colvec,xlim=c(0,1),ylim=c(0,1))