tgp (version 1.0-1)

dopt.gp: Sequential D-Optimal Design for a Stationary Gaussian Process

Description

Create sequential D-Optimal design for a stationary Gaussian process model of fixed parameterization by subsampling from a list of candidates

Usage

dopt.gp(nn, X, Xcand)

Arguments

nn

Number of new points in the design. Must be less than or equal to the number of candidates contained in Xcand, i.e., nn <= dim(xcand)[1]<="" code="">

X

data.frame, matrix or vector of input locations which are forced into (already in) the design.

Xcand

data.frame, matrix or vector of candidates from which new design points are subsampled. Must have the same dimension as X, i.e., dim(X)[2] == dim(Xcand)[2]

Value

• The output is a list which contains the inputs to and outputs of the C code used to find the optimal design. The chosen design locations are can be accessed as list members XX or equivalently Xcand[fi,].
• state
  unsigned short[3] random number seed to C
• X
  Input argument: data.frame of inputs X, can be NULL
• nn
  Input argument: number new points in the design
• n
  Number of rows in X, i.e., n = dim(X)[1]
• m
  Number of cols in X, i.e., m = dim(X)[2]
• Xcand
  Input argument: data.frame of candidate locations Xcand
• ncand
  Number of rows in Xcand, i.e., nncand = dim(Xcand)[1]
• fi
  Vector of length nn describing the selected new design locations as indices into XXcand
• XX
  data.frame of selected new design locations, i.e., XX = Xcand[fi,]

Details

Design is based on a stationary Gaussian process model with stationary isotropic exponential correlation function with parameterization fixed as a function of the dimension of the inputs. The algorithm implemented is a simple stochastic ascent which maximizes det(K)-- the covariance matrix constructed with locations X and a subset of Xcand of size nn. The selected design is locally optimal

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 http://www.ams.ucsc.edu/reports/trview.php?content=view&name=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/reports/trview.php?content=view&name=ams2005-17

http://people.ucsc.edu/~boobles/tgp.php

See Also

tgp.design, dopt.gp

Examples

#
# 2-d Exponential data
# (Contrast this with the tgp.design example,
# Also, 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

# find a treed sequential D-Optimal design 
# with 10 more points
dgp <- dopt.gp(10, X, Xcand)

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