NLogL_G {GPM}

The Function for calculating the gradient of Negative Log-Likelehood in GPM Package

Description

Calculates the gradient of negative log-likelihood wrt Omega.

Usage

NLogL_G(Omega, X, Y, CorrType, MinEig, Fn, n, dy)

Arguments

Omega

The vector storing all the hyperparameters of the correlation function. The length of Omega depends on the CorrType. See reference 1.

X

Matrix containing the training (aka design or input) data points. The rows and columns of X denote individual observation settings and input dimension, respectively.

Y

Matrix containing the output (aka response) data points. The rows and columns of Y denote individual observation responses and output dimension, respectively.

CorrType

The correlation function of the GP model. Choices include 'G' (default), 'PE', 'LBG', and 'LB'. See Fit and the references.

MinEig

The smallest eigen value that the correlation matrix is allowed to have, which in return determines the appraopriate nugget that should be added to the correlation matrix.

Fn

A matrix of 1's with nrow(X) rows and 1 column. See reference 1.

n

Number of observations, nrow(X).

dy

Number of responses, ncol(Y).

Details

This function is used in Fit if AnaGr != 0.

Value

NLogL_G The gradient of negative log-likelihood wrt Omega. See the references.

References

1. Bostanabad, R., Kearney, T., Tao, S., Apley, D. W. & Chen, W. (2018) Leveraging the nugget parameter for efficient Gaussian process modeling. Int J Numer Meth Eng, 114, 501-516.

2. Plumlee, M. & Apley, D. W. (2017) Lifted Brownian kriging models. Technometrics, 59, 165-177.

See Also

Fit to see how a GP model can be fitted to a training dataset.
Predict to use the fitted GP model for prediction.
Draw to plot the response via the fitted model.

Examples

# see the examples in the fitting function.