fit.GPModel: Fits a 'GPModel'

In gpboost: Combining Tree-Boosting with Gaussian Process and Mixed Effects Models

Fits a GPModel

Description

Estimates the parameters of a GPModel by maximizing the marginal likelihood

Usage

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

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 estimation / optimization optimizer_cov: string (default = "lbfgs"). Optimizer used for estimating covariance parameters. Options: "gradient_descent", "lbfgs", "fisher_scoring", "newton", "nelder_mead", "adam". If there are additional auxiliary parameters for non-Gaussian likelihoods, 'optimizer_cov' is also used for those optimizer_coef: string (default = "wls" for Gaussian likelihoods and "lbfgs" for other likelihoods). Optimizer used for estimating linear regression coefficients, if there are any (for the GPBoost algorithm there are usually none). Options: "gradient_descent", "lbfgs", "wls", "nelder_mead", "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. If 'optimizer_cov' is set to "nelder_mead", "lbfgs", or "adam", 'optimizer_coef' is automatically also set to the same value. maxit: integer (default = 1000). Maximal number of iterations for optimization algorithm delta_rel_conv: numeric (default = 1E-6 except for "nelder_mead" for which the default is 1E-8). Convergence tolerance. The algorithm stops if the relative change in either the (approximate) log-likelihood or the parameters is below this value. For "adam", the L2 norm of the gradient is used instead of the relative change in the log-likelihood. If < 0, internal default values are used convergence_criterion: string (default = "relative_change_in_log_likelihood"). The convergence criterion used for terminating the optimization algorithm. Options: "relative_change_in_log_likelihood" or "relative_change_in_parameters" init_coef: vector with numeric elements (default = NULL). Initial values for the regression coefficients (if there are any, can be NULL) init_cov_pars: vector with numeric elements (default = NULL). Initial values for covariance parameters of Gaussian process and random effects (can be NULL). The order it the same as the order of the parameters in the summary function: first is the error variance (only for "gaussian" likelihood), next follow the variances of the grouped random effects (if there are any, in the order provided in 'group_data'), and then follow the marginal variance and the range of the Gaussian process. If there are multiple Gaussian processes, then the variances and ranges follow alternatingly. If 'init_cov_pars = NULL', an internal choice is used that depends on the likelihood and the random effects type and covariance function. If you select the option 'trace = TRUE' in the 'params' argument, you will see the first initial covariance parameters in iteration 0. lr_coef: numeric (default = 0.1). Learning rate for fixed effect regression coefficients if gradient descent is used lr_cov: numeric (default = 0.1 for "gradient_descent" and 1. otherwise). Initial learning rate for covariance parameters if a gradient-based optimization method is used If lr_cov < 0, internal default values are used (0.1 for "gradient_descent" and 1. otherwise) If there are additional auxiliary parameters for non-Gaussian likelihoods, 'lr_cov' is also used for those For "lbfgs", this is divided by the norm of the gradient in the first iteration use_nesterov_acc: boolean (default = TRUE). If TRUE Nesterov acceleration is used. This is used only for gradient descent acc_rate_coef: numeric (default = 0.5). Acceleration rate for regression coefficients (if there are any) for Nesterov acceleration acc_rate_cov: numeric (default = 0.5). Acceleration rate for covariance parameters for Nesterov acceleration momentum_offset: integer (Default = 2). Number of iterations for which no momentum is applied in the beginning. trace: boolean (default = FALSE). If TRUE, information on the progress of the parameter optimization is printed std_dev: boolean (default = TRUE). 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) init_aux_pars: vector with numeric elements (default = NULL). Initial values for additional parameters for non-Gaussian likelihoods (e.g., shape parameter of a gamma or negative_binomial likelihood) estimate_aux_pars: boolean (default = TRUE). If TRUE, additional parameters for non-Gaussian likelihoods are also estimated (e.g., shape parameter of a gamma or negative_binomial likelihood) cg_max_num_it: integer (default = 1000). Maximal number of iterations for conjugate gradient algorithms cg_max_num_it_tridiag: integer (default = 1000). Maximal number of iterations for conjugate gradient algorithm when being run as Lanczos algorithm for tridiagonalization cg_delta_conv: numeric (default = 1E-2). Tolerance level for L2 norm of residuals for checking convergence in conjugate gradient algorithm when being used for parameter estimation num_rand_vec_trace: integer (default = 50). Number of random vectors (e.g., Rademacher) for stochastic approximation of the trace of a matrix reuse_rand_vec_trace: boolean (default = TRUE). If true, random vectors (e.g., Rademacher) for stochastic approximations of the trace of a matrix are sampled only once at the beginning of the parameter estimation and reused in later trace approximations. Otherwise they are sampled every time a trace is calculated seed_rand_vec_trace: integer (default = 1). Seed number to generate random vectors (e.g., Rademacher) piv_chol_rank: integer (default = 50). Rank of the pivoted Cholesky decomposition used as preconditioner in conjugate gradient algorithms cg_preconditioner_type: string. Type of preconditioner used for conjugate gradient algorithms. Options for non-Gaussian likelihoods and gp_approx = "vecchia": "Sigma_inv_plus_BtWB" (= default): (B^T * (D^-1 + W) * B) as preconditioner for inverting (B^T * D^-1 * B + W), where B^T * D^-1 * B approx= Sigma^-1 "piv_chol_on_Sigma": (Lk * Lk^T + W^-1) as preconditioner for inverting (B^-1 * D * B^-T + W^-1), where Lk is a low-rank pivoted Cholesky approximation for Sigma and B^-1 * D * B^-T approx= Sigma Options for likelihood = "gaussian" and gp_approx = "full_scale_tapering": "predictive_process_plus_diagonal" (= default): predictive process preconditiioner "none": no preconditioner
offset	A numeric vector with additional fixed effects contributions that are added to the linear predictor (= offset). The length of this vector needs to equal the number of training data points.
fixed_effects	This is discontinued. Use the renamed equivalent argument offset instead

Value

A fitted GPModel

Author(s)

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
 
#--------------------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

gpboost documentation built on Sept. 11, 2024, 7:04 p.m.