tgp.design {tgp}R Documentation

Sequential Treed D-Optimal Design for Treed Gaussian Process Models

Description

Based on the maximum a' posteriori (MAP) treed partition extracted from a "tgp"-class object, calculate independant sequential treed D-Optimal designs in each of the regions.

Usage

tgp.design(howmany, Xcand, out)

Arguments

howmany Number of new points in the design. Must be less than the number of candidates contained in Xcand, i.e., howmany <= dim(Xcand)[1]
Xcand data.frame, matrix or vector of candidates from which new design points are subsampled. Must have the same dimension as out$X
out "tgp" class object which is the output of one of the model functions which has tree support, e.g., btgpllm, btgp, btlm, or tgp

Details

This function partitions Xcand and out$X based on the MAP tree (obtained on "tgp"-class out with tgp.get.partitions) and calls dopt.gp in order to obtain a D-optimal design under independent stationary Gaussian processes models defined in each region. The aim is to obtain a design where new points from Xcand are spaced out relative to themselves, and relative to the existing locations (out$X) in the region. The number of new points from each region is proportional to the number of candidates Xcand in the region.

Value

Output is a list of data.frames containing XX design points for each region of the MAP tree in out

Note

Input Xcand containing NaN, NA, Inf are discarded with non-fatal warnings

D-Optimal computation in each region is preceded by a print statement indicated the number of new locations to be chosen and the number of candidates in the region. Other than that, there are no other indicators of progress. You will have to be patient. Creating treed sequential D-optimal designs is no speedy task. At least it faster than the non-treed version (see dopt.gp).

This function is still considered experimental. (Pardon the pun.)

The example below is also part of vignette("tgp")

Author(s)

Robert B. Gramacy rbgramacy@ams.ucsc.edu

References

Gramacy, R. B., Lee, H. K. H., & Macready, W. (2004). Parameter space exploration with Gaussian process trees. ICML (pp. 353–360). Omnipress & ACM Digital Library.

Gramacy, R. B., Lee, H. K. H., & Macready, W. (2005). Adaptive Exploration of Computer Experiment Parameter Spaces. submitted to JCGS, available as UCSC Technical Report ams2005-16

Gramacy, R. B. & Lee, H. K. H. (2005). Gaussian Processes and Limiting Linear Models. available as UCSC Technical Report ams2005-17

http://www.ams.ucsc.edu/~rbgramacy/tgp.php

See Also

bgpllm, btlm, blm, bgp, btgpllm, tgp, plot.tgp, dopt.gp, tgp.get.partitions

Examples

#
# 2-d Exponential data
# (This example is based on random data.  
# It might be fun to run it a few times)
#

# get the data
exp2d.data <- exp2d.rand()
X <- exp2d.data$X; Z <- exp2d.data$Z
Xcand <- exp2d.data$XX

# fit treed GP LLM model to data w/o prediction
# basically just to get MAP tree (and plot it)
out <- btgpllm(X=X, Z=Z, pred.n=FALSE, corr="exp")
tgp.trees(out)

# find a treed sequential D-Optimal design 
# with 10 more points.  It is interesting to 
# contrast this design with one obtained via
# the dopt.gp function
XX <- tgp.design(10, Xcand, out)

# now fit the model again in order to assess
# the predictive surface at those new design points
dout <- btgpllm(X=X, Z=Z, XX=XX, corr="exp")
plot(dout)

[Package tgp version 1.1-3 Index]