Description Usage Arguments Value References See Also Examples

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.

1 2 3 4 5 |

`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 ( |

`lb_phi_lat, ub_phi_lat` |
The later lower and upper search bounds of the scale/roughness parameters ( |

`lb_z, ub_z` |
The lower and upper search bounds of the latent parameters ( |

`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 |

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

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

`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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
# 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)
``` |

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