exp2d.rand
Random 2-d Exponential Data
A Random subsample of data(exp2d)
, or
Latin Hypercube sampled data evaluated with exp2d.Z
Usage
exp2d.rand(n1 = 50, n2 = 30, lh = NULL, dopt = 1)
Arguments
- 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 fromdata(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 ofdopt
will be used. This argument only makes sense when!is.null(lh)
Details
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
$$Z(X)=x_1 * \exp(x_1^2-x_2^2).$$
thus creating the outputs Ztrue
and ZZtrue
.
Zero-mean normal noise with sd=0.001
is added to the
responses Z
and ZZ
Value
Output is a list
with entries:
2-d data.frame
with n1 + n2
input locations
Numeric vector describing the responses (with noise) at the
X
input locations
Numeric vector describing the true responses (without
noise) at the X
input locations
2-d data.frame
containing the remaining
441 - (n1 + n2)
input locations
Numeric vector describing the responses (with noise) at
the XX
predictive locations
Numeric vector describing the responses (without
noise) at the XX
predictive locations
References
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). https://www.jstatsoft.org/v19/i09
Gramacy, R. B., Lee, H. K. H. (2008). Bayesian treed Gaussian process models with an application to computer modeling. Journal of the American Statistical Association, 103(483), pp. 1119-1130. Also available as ArXiv article 0710.4536 https://arxiv.org/abs/0710.4536
See Also
Examples
# NOT RUN {
## 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)
# }