modelKrigingLikelihood: Calculate negative log-likelihood

In CEGO: Combinatorial Efficient Global Optimization

Description

Used to determine theta/lambda/p values for the Kriging model in modelKriging with Maximum Likelihood Estimation (MLE).

Usage

modelKrigingLikelihood(
  xt,
  D,
  y,
  useLambda = FALSE,
  corr = fcorrGauss,
  indefiniteMethod = "none",
  indefiniteType = "PSD",
  indefiniteRepair = FALSE,
  returnLikelihoodOnly = TRUE,
  inverter = "chol",
  ntheta = 1
)

Arguments

xt	vector, containing parameters like theta, p and lambda.
D	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.
y	vector of observations at sample locations.
useLambda	whether to use nugget effect, i.e., lambda (FALSE at default).
corr	whether to use nugget effect, i.e., lambda (fcorrGauss at default).
indefiniteMethod	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).
indefiniteType	The general type of correction for indefiniteness: "NSD","CNSD" or the default "PSD". See Zaefferer and Bartz-Beielstein (2016).
indefiniteRepair	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.
returnLikelihoodOnly	boolean, whether the function should return only the likelihood, or a else a list (see return information below).
inverter	string, defining the inverter to use. default "chol" is inversion via chol2inv. A different string will lead to use of solve.
ntheta	number of kernel parameters.

Value

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

References

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.

See Also

modelKriging

CEGO documentation built on May 14, 2021, 1:08 a.m.