kernDeepStackNet (version 2.0.2)

predLogProb: Predictive logarithmic probability of Kriging model

Description

Calculates the predictive logarithmic probability of Kriging model given the model parameters (likelihood function). It is used to choose better meta models in model-based optimization using Kriging. The observation used for prediction is left out in the training data and then estimated.

Usage

predLogProb(predMean, predSigma, y, X)

Arguments

predMean

Predicted leave one out mean of the Kriging model of all observations (numeric vector).

predSigma

Predicted leave one out variance of the Kriging model of all observations.

y

Numeric response vector of the outcome. Should be formated as a one column matrix.

X

Numeric design matrix of the covariates. All factors have to be prior encoded.

Value

Numeric Value of log-likelihood with leave-one-out parameters.

Details

Gaussian processes are conditionaly normal distributed and therefore the normal likelihood is used. The leave out parameters can be efficiently computed without performing leave one out cross-validation.

References

Carl Edward Rasmussen and Christopher K. I. Williams, (2006), Gaussian Processes for Machine Learning Massachusetts Institute of Technology

Examples

library(DiceKriging)
# Generate design of experiments
design.fact <- expand.grid(x1=seq(0,1,length=4), x2=seq(0,1,length=4))
y <- apply(design.fact, 1, branin) 

# Estimate Kriging model
km_fit <- km(design=design.fact, response=y, control=list(trace=FALSE), 
nugget.estim=TRUE, iso=FALSE)

# Calculate leave one out parameters and performance measure
loo <- leaveOneOut.km(model=km_fit, type="UK", trend.reestim=TRUE)
predLogProbs <- predLogProb(predMean=loo$mean, predSigma=loo$sd^2, y=y, X=X)