neg_log_l {LVGP}

The Negative Log-Likelehood Function in LVGP Package

Description

Calculates the negative log-likelihood (excluding all the constant terms) as described in reference 1.

Usage

neg_log_l(hyperparam, p_quant, p_qual, lvs_qual, n_lvs_qual, dim_z,
  X_quant, X_qual, Y, min_eig, k, M)

Arguments

hyperparam

Hyperparameters of the LVGP model

p_quant

Number of quantative variables

p_qual

Number of qualitative variables

lvs_qual

Levels of each qualitative variable

n_lvs_qual

Number of levels of each qualitative variable

dim_z

Dimensionality of latent variables, usually 1 or 2

X_quant

Input data of quantative variables

X_qual

Input data of qualitative variables

Y

Vector containing the outputs of data points

min_eig

The smallest eigen value that the correlation matrix is allowed to have, which determines the nugget added to the correlation matrix.

k

Number of data points, nrow(X_quant) or nrow(X_qual)

M

Vector of ones with length k

Details

LVGP_fit calls this function as its optimization objective function.

Value

The negative log-likelihood (excluding all the constant terms) value.

Note

This function is NOT exported once the package is loaded.

References

1. "A Latent Variable Approach to Gaussian Process Modeling with Qualitative and Quantitative Factors", Yichi Zhang, Siyu Tao, Wei Chen, and Daniel W. Apley (arXiv)

See Also

LVGP_fit to see how a GP model can be fitted to a training dataset.
LVGP_predict to use the fitted LVGP model for prediction.
LVGP_plot to plot the features of the fitted model.

Examples

# see the examples in the documentation of the function LVGP_fit.