exp2d.rand {tgp} | R Documentation |
A Random subsample of data(exp2d)
, or
Latin Hypercube sampled data evaluated with exp2d.Z
exp2d.rand(n1 = 50, n2 = 30, lh = NULL, dopt = 1)
n1 |
Number of samples from the first, interesting, quadrant |
n2 |
Number of samples from the other three, uninteresting, quadrants |
lh |
If !is.null(lh) then Latin Hypercube (LH) sampling
(lhs ) is used instead of subsampling from
data(exp2d) ; lh should be a single nonnegative
integer specifying the desired number of predictive locations,
XX ; or, it should be a vector of length 4, specifying the
number of predictive locations desired from each of the four
quadrants (interesting quadrant first, then counter-clockwise) |
dopt |
If dopt >= 2 then d-optimal subsampling from LH
candidates of the multiple indicated by the value of
dopt will be used. This argument only
makes sense when !is.null(lh) |
When is.null(lh)
, data is subsampled without replacement from
data(exp2d)
. Of the n1 + n2 <= 441
input/response pairs X,Z
, there are n1
are taken from the
first quadrant, i.e., where the response is interesting,
and the remaining n2
are taken from the other three
quadrants. The remaining 441 - (n1 + n2)
are treated as
predictive locations
Otherwise, when !is.null(lh)
, Latin Hypercube Sampling
(lhs
) is used
If dopt >= 2
then n1*dopt
LH candidates are used
for to get a D-optimal subsample of size n1
from the
first (interesting) quadrant. Similarly n2*dopt
in the
rest of the un-interesting region.
A total of lh*dopt
candidates will be used for sequential D-optimal
subsampling for predictive locations XX
in all four
quadrants assuming the already-sampled X
locations will
be in the design.
In all three cases, the response is evaluated as
Z(X) = X1 * exp(-X1^2 -X2^2),
thus creating the outputs Ztrue
and ZZtrue
.
Zero-mean normal noise with sd=0.001
is added to the
responses Z
and ZZ
Output is a list
with entries:
X |
2-d data.frame with n1 + n2 input locations |
Z |
Numeric vector describing the responses (with noise) at the
X input locations |
Ztrue |
Numeric vector describing the true responses (without
noise) at the X input locations |
XX |
2-d data.frame containing the remaining
441 - (n1 + n2) input locations |
ZZ |
Numeric vector describing the responses (with noise) at
the XX predictive locations |
ZZtrue |
Numeric vector describing the responses (without
noise) at the XX predictive locations |
Gramacy, R. B., Lee, H. K. H. (2006). Bayesian treed Gaussian process models. Available as UCSC Technical Report ams2006-01.
http://www.ams.ucsc.edu/~rbgramacy/tgp.html
lhs
, exp2d
, exp2d.Z
,
btgp
, and other b*
functions
## randomly subsampled data ## ------------------------ eds <- exp2d.rand() # higher span = 0.5 required because the data is sparse # and was generated randomly eds.g <- interp.loess(eds$X[,1], eds$X[,2], eds$Z, span=0.5) # perspective plot, and plot of the input (X & XX) locations par(mfrow=c(1,2), bty="n") persp(eds.g, main="loess surface", theta=-30, phi=20, xlab="X[,1]", ylab="X[,2]", zlab="Z") plot(eds$X, main="Randomly Subsampled Inputs") points(eds$XX, pch=19, cex=0.5) ## Latin Hypercube sampled data ## ---------------------------- edlh <- exp2d.rand(lh=c(20, 15, 10, 5)) # higher span = 0.5 required because the data is sparse # and was generated randomly edlh.g <- interp.loess(edlh$X[,1], edlh$X[,2], edlh$Z, span=0.5) # perspective plot, and plot of the input (X & XX) locations par(mfrow=c(1,2), bty="n") persp(edlh.g, main="loess surface", theta=-30, phi=20, xlab="X[,1]", ylab="X[,2]", zlab="Z") plot(edlh$X, main="Latin Hypercube Sampled Inputs") points(edlh$XX, pch=19, cex=0.5) # show the quadrants abline(h=2, col=2, lty=2, lwd=2) abline(v=2, col=2, lty=2, lwd=2) ## Not run: ## D-optimal subsample with a factor of 10 (more) candidates ## --------------------------------------------------------- edlhd <- exp2d.rand(lh=c(20, 15, 10, 5), dopt=10) # higher span = 0.5 required because the data is sparse # and was generated randomly edlhd.g <- interp.loess(edlhd$X[,1], edlhd$X[,2], edlhd$Z, span=0.5) # perspective plot, and plot of the input (X & XX) locations par(mfrow=c(1,2), bty="n") persp(edlhd.g, main="loess surface", theta=-30, phi=20, xlab="X[,1]", ylab="X[,2]", zlab="Z") plot(edlhd$X, main="D-optimally Sampled Inputs") points(edlhd$XX, pch=19, cex=0.5) # show the quadrants abline(h=2, col=2, lty=2, lwd=2) abline(v=2, col=2, lty=2, lwd=2) ## End(Not run)