Used to determine theta/lambda/p values for the Kriging model in modelKriging
with Maximum Likelihood Estimation (MLE).
modelKrigingLikelihood(xt, D, y, optimizeP = FALSE, useLambda = FALSE,
corr = fcorrGauss, indefiniteMethod = "none", indefiniteType = "PSD",
indefiniteRepair = FALSE, returnLikelihoodOnly = TRUE)vector, containing parameters like log10(theta), p and lambda.
matrix (or list of multiple matrices) of distances between training samples. In case of multiple distance matrices, theta (part of xt) has to be a vector, giving a weighting parameter for each matrix.
vector of observations at sample locations.
whether to optimize p or not (FALSE at default).
whether to use nugget effect, i.e., lambda (FALSE at default).
whether to use nugget effect, i.e., lambda (fcorrGauss at default).
The specific method used for correction: spectrum "clip", spectrum "flip", spectrum "square", spectrum "diffusion", feature embedding "feature", nearest definite matrix "near". Default is no correction: "none". See Zaefferer and Bartz-Beielstein (2016).
The general type of correction for indefiniteness: "NSD","CNSD" or the default "PSD". See Zaefferer and Bartz-Beielstein (2016).
boolean, whether conditions of the distance matrix (in case of "NSD","CNSD" correction type) or correlation matrix (in case of "PSD" correction type) are repaired.
boolean, whether the function should return only the likelihood, or a else a list (see return information below).
the numeric Likelihood value (if returnLikelihoodOnly is TRUE) or a list with elements
NegLnLike concentrated log-likelihood *-1 for minimising
Psi correlation matrix
Psinv inverse of correlation matrix (to save computation time in forrRegPredictor)
mu MLE of model parameter mu
yMu vector of observations y minus mu
SSQ MLE of model parameter sigma^2
a transformation vector for eigenspectrum transformation, see Zaefferer and Bartz-Beielstein (2016)
U Matrix of eigenvectors for eigenspectrum transformation, see Zaefferer and Bartz-Beielstein (2016)
isIndefinite whether the uncorrected correlation (kernel) matrix is indefinite
Forrester, Alexander I.J.; Sobester, Andras; Keane, Andy J. (2008). Engineering Design via Surrogate Modelling - A Practical Guide. John Wiley & Sons.
Zaefferer, Martin; Stork, Joerg; Friese, Martina; Fischbach, Andreas; Naujoks, Boris; Bartz-Beielstein, Thomas. (2014). Efficient global optimization for combinatorial problems. In Proceedings of the 2014 conference on Genetic and evolutionary computation (GECCO '14). ACM, New York, NY, USA, 871-878. DOI=10.1145/2576768.2598282 http://doi.acm.org/10.1145/2576768.2598282
Zaefferer, Martin; Stork, Joerg; Bartz-Beielstein, Thomas. (2014). Distance Measures for Permutations in Combinatorial Efficient Global Optimization. In Parallel Problem Solving from Nature - PPSN XIII (p. 373-383). Springer International Publishing.
Martin Zaefferer and Thomas Bartz-Beielstein. (2016). Efficient Global Optimization with Indefinite Kernels. Parallel Problem Solving from Nature-PPSN XIV. Accepted, in press. Springer.