Used to determine theta/lambda/p values for the Kriging model in modelKriging
with Maximum Likelihood Estimation (MLE).
modelKrigingLikelihood(
xt,
D,
y,
useLambda = FALSE,
corr = fcorrGauss,
indefiniteMethod = "none",
indefiniteType = "PSD",
indefiniteRepair = FALSE,
returnLikelihoodOnly = TRUE,
inverter = "chol",
ntheta = 1
)the numeric Likelihood value (if returnLikelihoodOnly is TRUE) or a list with elements:
NegLnLikeconcentrated log-likelihood *-1 for minimising
Psicorrelation matrix
Psinvinverse of correlation matrix (to save computation time in forrRegPredictor)
muMLE of model parameter mu
yMuvector of observations y minus mu
SSQMLE of model parameter sigma^2
atransformation vector for eigenspectrum transformation, see Zaefferer and Bartz-Beielstein (2016)
UMatrix of eigenvectors for eigenspectrum transformation, see Zaefferer and Bartz-Beielstein (2016)
isIndefinitewhether the uncorrected correlation (kernel) matrix is indefinite
vector, containing parameters like 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 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).
string, defining the inverter to use. default "chol" is inversion via chol2inv. A different string will lead to use of solve.
number of kernel parameters.
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
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.
modelKriging