CEGO: modelKrigingLikelihood – R documentation

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modelKrigingLikelihood

Calculate negative log-likelihood

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 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.

modelKrigingLikelihood

Description

Usage

Arguments

Value

References

See Also

CEGO

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