gpboost (version 0.7.9)

fit.GPModel: Fits a GPModel

Description

Estimates the parameters of a GPModel using maximum likelihood estimation

Usage

# S3 method for GPModel
fit(gp_model, y, X = NULL, params = list(),
  fixed_effects = NULL)

Value

A fitted GPModel

Arguments

gp_model

a GPModel

y

A vector with response variable data

X

A matrix with numeric covariate data for the fixed effects linear regression term (if there is one)

params

A list with parameters for the model fitting / optimization

• optimizer_cov Optimizer used for estimating covariance parameters. Options: "gradient_descent", "fisher_scoring", "nelder_mead", "bfgs", "adam". Default= gradient_descent"

• optimizer_coef Optimizer used for estimating linear regression coefficients, if there are any (for the GPBoost algorithm there are usually none). Options: "gradient_descent", "wls", "nelder_mead", "bfgs", "adam". Gradient descent steps are done simultaneously with gradient descent steps for the covariance parameters. "wls" refers to doing coordinate descent for the regression coefficients using weighted least squares. Default="wls" for Gaussian data and "gradient_descent" for other likelihoods. If 'optimizer_cov' is set to "nelder_mead", "bfgs", or "adam", 'optimizer_coef' is automatically also set to the same value.

• maxit Maximal number of iterations for optimization algorithm. Default=1000

• delta_rel_conv Convergence tolerance. The algorithm stops if the relative change in eiher the (approximate) log-likelihood or the parameters is below this value. For "bfgs" and "adam", the L2 norm of the gradient is used instead of the relative change in the log-likelihood. Default=1E-6

• convergence_criterion The convergence criterion used for terminating the optimization algorithm. Options: "relative_change_in_log_likelihood" (default) or "relative_change_in_parameters"

• init_coef Initial values for the regression coefficients (if there are any, can be NULL). Default=NULL

• init_cov_pars Initial values for covariance parameters of Gaussian process and random effects (can be NULL). Default=NULL

• lr_coef Learning rate for fixed effect regression coefficients if gradient descent is used. Default=0.1

• lr_cov Learning rate for covariance parameters. If <= 0, internal default values are used. Default value = 0.1 for "gradient_descent" and 1. for "fisher_scoring"

• use_nesterov_acc If TRUE Nesterov acceleration is used. This is used only for gradient descent. Default=TRUE

• acc_rate_coef Acceleration rate for regression coefficients (if there are any) for Nesterov acceleration. Default=0.5

• acc_rate_cov Acceleration rate for covariance parameters for Nesterov acceleration. Default=0.5

• momentum_offset Number of iterations for which no momentum is applied in the beginning. Default=2

• trace If TRUE, information on the progress of the parameter optimization is printed. Default=FALSE

• std_dev If TRUE, approximate standard deviations are calculated for the covariance and linear regression parameters (= square root of diagonal of the inverse Fisher information for Gaussian likelihoods and square root of diagonal of a numerically approximated inverse Hessian for non-Gaussian likelihoods)

fixed_effects

A vector of optional external fixed effects which are held fixed during training.

Author

Fabio Sigrist

Examples

# See https://github.com/fabsig/GPBoost/tree/master/R-package for more examples

data(GPBoost_data, package = "gpboost")
# Add intercept column
X1 <- cbind(rep(1,dim(X)[1]),X)
X_test1 <- cbind(rep(1,dim(X_test)[1]),X_test)

#--------------------Grouped random effects model: single-level random effect----------------
gp_model <- GPModel(group_data = group_data[,1], likelihood="gaussian")
fit(gp_model, y = y, X = X1, params = list(std_dev = TRUE))
summary(gp_model)
# Make predictions
pred <- predict(gp_model, group_data_pred = group_data_test[,1], 
                X_pred = X_test1, predict_var = TRUE)
pred$mu # Predicted mean
pred$var # Predicted variances
# Also predict covariance matrix
pred <- predict(gp_model, group_data_pred = group_data_test[,1], 
                X_pred = X_test1, predict_cov_mat = TRUE)
pred$mu # Predicted mean
pred$cov # Predicted covariance
 
# \donttest{
#--------------------Gaussian process model----------------
gp_model <- GPModel(gp_coords = coords, cov_function = "exponential",
                    likelihood="gaussian")
fit(gp_model, y = y, X = X1, params = list(std_dev = TRUE))
summary(gp_model)
# Make predictions
pred <- predict(gp_model, gp_coords_pred = coords_test, 
                X_pred = X_test1, predict_cov_mat = TRUE)
pred$mu # Predicted (posterior) mean of GP
pred$cov # Predicted (posterior) covariance matrix of GP
# }