LVGP_fit: The Fitting Function of 'LVGP' Package

In LVGP: Latent Variable Gaussian Process Modeling with Qualitative and Quantitative Input Variables

Description

Fits a latent-variable Gaussian process (LVGP) model to a dataset as described in reference 1. The input variables can be quantitative or qualitative/categorical or mixed. The output variable is quantitative and scalar.

Usage

LVGP_fit(X, Y, ind_qual = NULL, dim_z = 2, eps = 10^(seq(-1, -8,
  length.out = 15)), lb_phi_ini = -2, ub_phi_ini = 2,
  lb_phi_lat = -8, ub_phi_lat = 3, lb_z = -3, ub_z = 3,
  n_opt = 8, max_iter_ini = 100, max_iter_lat = 20, seed = 123,
  progress = FALSE, parallel = FALSE, noise = FALSE)

Arguments

X	Matrix or data frame containing the inputs of training data points. Each row is a data point.
Y	Vector containing the outputs of training data points
ind_qual	Vector containing the indices of columns of qualitative/categorical variables
dim_z	Dimensionality of latent space, usually 1 or 2 but can be higher
eps	The vector of smallest eigen values that the correlation matrix is allowed to have, which determines the nugget added to the correlation matrix.
lb_phi_ini, ub_phi_ini	The initial lower and upper search bounds of the scale/roughness parameters (phi) of quantitative variables
lb_phi_lat, ub_phi_lat	The later lower and upper search bounds of the scale/roughness parameters (phi) of quantitative variables
lb_z, ub_z	The lower and upper search bounds of the latent parameters (z) of qualitative variables
n_opt	The number of times the log-likelihood function is optimized
max_iter_ini	The maximum number of iterations for each optimization run for largest (first) eps case
max_iter_lat	The maximum number of iterations for each optimization run for after first eps cases
seed	An integer for the random number generator. Use this to make the results reproducible.
progress	The switch determining whether to print function run details
parallel	The switch determining whether to use parallel computing
noise	The switch for whether the data are assumed noisy

Value

A model of class "LVGP model" list of the following items:

• quant_param A list containing the estimated parameter phi and its search bounds for quantitative variables

• qual_param A list containing the estimated parameter z and its dimensionality, vectorized form and search bounds for qualitative variables

• data A list containing the fitted dataset in verbose format

• fit_detail A list of more detailed variables for fitting and prediction process

• optim_hist Optimization history

• setting Settings for the optimization and fitting process

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

optim for the details on L-BFGS-B algorithm used in optimization.
LVGP_predict to use the fitted LVGP model for prediction.
LVGP_plot to plot the features of the fitted model.

Examples

# Math example with 2 quantitative and 1 qualitative variables (dataset included in the package):
#     Fit a model (with default settings) and evaluate the performance
#     by computing the root mean squared error (RMSE) in prediction.
#     Also, plot the latent variable parameters.
X_tr <- math_example$X_tr
Y_tr <- math_example$Y_tr
X_te <- math_example$X_te
Y_te <- math_example$Y_te
n_te <- nrow(X_te)
model <- LVGP_fit(X_tr, Y_tr, ind_qual = c(3))
output <- LVGP_predict(X_te, model)
Y_hat <- output$Y_hat
RRMSE <- sqrt(sum((Y_hat-Y_te)^2)/n_te)/(max(Y_te)-min(Y_te))
LVGP_plot(model)

LVGP documentation built on May 1, 2019, 7:05 p.m.