Black box optimization and response surface exploration

Description

blackbox allows prediction and optimization of a response function from simulated response values. It also includes procedures designed mainly or only to be called, in a completely automated way without any input by users, by other R packages such as the Infusion package (under development) or by R code automatically generated by the Migraine software (see Details). For prediction, blackbox interfaces a C++ library for “ordinary Kriging” (which is jargon for: prediction in a linear mixed model with a constant term as fixed effect). It uses generalized cross validation (GCV) by default to estimate smoothing parameters.

Details

Beyond the usage illustrated below, this package is used in particular for smoothing the output of the Migraine software for likelihood analysis of population genetic data (http://kimura.univ-montp2.fr/~rousset/Migraine.htm). In the latter application the response function is a simulated log-likelihood surface and the procedures generate plots of the (profile) log-likelihood, compute (profile) likelihood ratio confidence intervals, and design new parameter points where the likelihood should be simulated. This package provides documentation for all user-level functions in the R script written by Migraine. Control from Migraine uses many variables stored globally in the list of options accessible through blackbox.options().

The C++ DLL was originally a c++ reimplementation of some of the internal functions of the fields package, circa 2005-2006. To estimate smoothing parameters, it requires pairs of responses values for some values of the predictor variables, but will not allow more than pairs.

Author(s)

François Rousset, with contributions by Raphaël Leblois.

References

Chambers J.M. (2008) Software for data analysis: Programming with R. Springer-Verlag.

Fields Development Team (2006). fields: Tools for Spatial Data. National Center for Atmospheric Research, Boulder, CO. http://www.image.ucar.edu/GSP/Software/Fields/.

Examples

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fr <- function(v) { ## Rosenbrock Banana function with noise
  10 * (v["y"] - v["x"]^2)^2 + (1 - v["x"])^2 + rnorm(1,sd=0.1)
}
set.seed(123)

# Initial parameter values, including duplicates. See ?init_grid.
parsp <- init_grid(lower=c(x=0,y=0),upper=c(x=2,y=2))

# add function values
simuls <- cbind(parsp,bb=apply(parsp,1,"fr"))

## The following shows the backbone of the 'bboptim' code:

sorted_etc <- prepareData(data=simuls)
#   Then smoothing using GCV (beware of implicit 'decreasing=FALSE' argument)
gcvres <- calcGCV(sorted_etc)

## The results can be used as input to functions from other packages,
##  e.g. corrHLfit from spaMM:
## Not run: 
require(spaMM)
corrHLfit(bb ~ 1+Matern(1|x+y),data=sorted_etc,
          ranFix=list(rho=1/gcvres$CovFnParam[c("x", "y")],
          #         note '1/...'
                      nu=gcvres$CovFnParam[["smoothness"]],
                      phi=gcvres$pureRMSE^2,
          # note distinct meaning of lambda notation in spaMM and blackbox
                      lambda=with(gcvres,(pureRMSE^2)/lambdaEst)))

## GCV is distinct from an REML fit:
corrHLfit(bb ~ 1+Matern(1|x+y),data=sorted_etc,
          init.corrHLfit=list(rho=c(1,1)))

## End(Not run)