Sequential Treed D-Optimal Design for Treed Gaussian Process Models
Based on the maximum a' posteriori (MAP)
treed partition extracted from a
calculate independent sequential treed D-Optimal designs in each of the regions.
tgp.design(howmany, Xcand, out, iter = 5000, verb = 0)
Number of new points in the design. Must
be less than the number of candidates contained in
number of iterations of stochastic accent algorithm,
positive integer indicating after how many rounds of
stochastic approximation in
This function partitions
out$X based on
the MAP tree (obtained on
partition) and calls
dopt.gp in order to obtain a D-optimal design under
independent stationary Gaussian processes models defined in each
region. The aim is to obtain a design where new points from
are spaced out relative to themselves, and relative to
the existing locations (
out$X) in the region.
The number of new points from each region of the partition is
proportional to the number of candidates
Xcand in the region.
Output is a list of
points for each region of the MAP tree in
NaN, NA, Inf are discarded with non-fatal
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
The example below is also part of
vignette("tgp2") for a similar example based on
optimization using the
Gramacy, R. B. (2007). tgp: An R Package for Bayesian Nonstationary, Semiparametric Nonlinear Regression and Design by Treed Gaussian Process Models. Journal of Statistical Software, 19(9). http://www.jstatsoft.org/v19/i09
Robert B. Gramacy, Matthew Taddy (2010). Categorical Inputs, Sensitivity Analysis, Optimization and Importance Tempering with tgp Version 2, an R Package for Treed Gaussian Process Models. Journal of Statistical Software, 33(6), 1–48. http://www.jstatsoft.org/v33/i06/.
Gramacy, R. B., Lee, H. K. H. (2006). Adaptive design and analysis of supercomputer experiments. Technometrics, to appear. Also avaliable on ArXiv article 0805.4359 http://arxiv.org/abs/0805.4359
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.
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# # 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)
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