GPModel, gpb.cv, and gpboostDocumentation for parameters shared by GPModel, gpb.cv, and gpboost
A string specifying the likelihood function (distribution) of the response variable.
Available options:
"gaussian"
"bernoulli_probit": binary data with Bernoulli likelihood and a probit link function
"bernoulli_logit": binary data with Bernoulli likelihood and a logit link function
"gamma": gamma distribution with a with log link function
"poisson": Poisson distribution with a with log link function
"negative_binomial": negative binomial distribution with a with log link function
"t": t-distribution (e.g., for robust regression)
"t_fix_df": t-distribution with the degrees-of-freedom (df) held fixed and not estimated.
The df can be set via the likelihood_additional_param parameter
Note: other likelihoods could be implemented upon request
A numeric specifying an additional parameter for the likelihood
which cannot be estimated for this likelihood (e.g., degrees of freedom for likelihood = "t_fix_df").
This is not to be confused with any auxiliary parameters that can be estimated and accessed through
the function get_aux_pars after estimation.
Note that this likelihood_additional_param parameter is irrelevant for many likelihoods.
If likelihood_additional_param = NULL, the following internal default values are used:
df = 2 for likelihood = "t_fix_df"
A vector or matrix whose columns are categorical grouping variables.
The elements being group levels defining grouped random effects.
The elements of 'group_data' can be integer, double, or character.
The number of columns corresponds to the number of grouped (intercept) random effects
A vector or matrix with numeric covariate data
for grouped random coefficients
A vector with integer indices that
indicate the corresponding categorical grouping variable (=columns) in 'group_data' for
every covariate in 'group_rand_coef_data'. Counting starts at 1.
The length of this index vector must equal the number of covariates in 'group_rand_coef_data'.
For instance, c(1,1,2) means that the first two covariates (=first two columns) in 'group_rand_coef_data'
have random coefficients corresponding to the first categorical grouping variable (=first column) in 'group_data',
and the third covariate (=third column) in 'group_rand_coef_data' has a random coefficient
corresponding to the second grouping variable (=second column) in 'group_data'
A vector of type logical (boolean).
Indicates whether intercept random effects are dropped (only for random coefficients).
If drop_intercept_group_rand_effect[k] is TRUE, the intercept random effect number k is dropped / not included.
Only random effects with random slopes can be dropped.
A matrix with numeric coordinates (= inputs / features) for defining Gaussian processes
A vector or matrix with numeric covariate data for
Gaussian process random coefficients
A string specifying the covariance function for the Gaussian process.
Available options:
"exponential": Exponential covariance function (using the parametrization of Diggle and Ribeiro, 2007)
"gaussian": Gaussian, aka squared exponential, covariance function (using the parametrization of Diggle and Ribeiro, 2007)
"matern": Matern covariance function with the smoothness specified by
the cov_fct_shape parameter (using the parametrization of Rasmussen and Williams, 2006)
"powered_exponential": powered exponential covariance function with the exponent specified by
the cov_fct_shape parameter (using the parametrization of Diggle and Ribeiro, 2007)
"wendland": Compactly supported Wendland covariance function (using the parametrization of Bevilacqua et al., 2019, AOS)
"matern_space_time": Spatio-temporal Matern covariance function with different range parameters for space and time.
Note that the first column in gp_coords must correspond to the time dimension
"matern_ard": anisotropic Matern covariance function with Automatic Relevance Determination (ARD),
i.e., with a different range parameter for every coordinate dimension / column of gp_coords
"gaussian_ard": anisotropic Gaussian, aka squared exponential, covariance function with Automatic Relevance Determination (ARD),
i.e., with a different range parameter for every coordinate dimension / column of gp_coords
A numeric specifying the shape parameter of the covariance function
(=smoothness parameter for Matern covariance)
This parameter is irrelevant for some covariance functions such as the exponential or Gaussian
A string specifying the large data approximation
for Gaussian processes. Available options:
"none": No approximation
"vecchia": A Vecchia approximation; see Sigrist (2022, JMLR) for more details
"tapering": The covariance function is multiplied by a compactly supported Wendland correlation function
"fitc": Fully Independent Training Conditional approximation aka modified predictive process approximation; see Gyger, Furrer, and Sigrist (2024) for more details
"full_scale_tapering": A full scale approximation combining an inducing point / predictive process approximation with tapering on the residual process; see Gyger, Furrer, and Sigrist (2024) for more details
"vecchia_latent": similar as "vecchia" but a Vecchia approximation is applied to the latent Gaussian process for likelihood == "gaussian". For likelihood != "gaussian", "vecchia" and "vecchia_latent" are equivalent
An integer specifying the number of parallel threads for OMP.
If num_parallel_threads = NULL, all available threads are used
A numeric specifying the range parameter
of the Wendland covariance function and Wendland correlation taper function.
We follow the notation of Bevilacqua et al. (2019, AOS)
A numeric specifying the shape (=smoothness) parameter
of the Wendland covariance function and Wendland correlation taper function.
We follow the notation of Bevilacqua et al. (2019, AOS)
An integer specifying the number of neighbors for
the Vecchia approximation. Note: for prediction, the number of neighbors can
be set through the 'num_neighbors_pred' parameter in the 'set_prediction_data'
function. By default, num_neighbors_pred = 2 * num_neighbors. Further,
the type of Vecchia approximation used for making predictions is set through
the 'vecchia_pred_type' parameter in the 'set_prediction_data' function
A string specifying the ordering used in
the Vecchia approximation. Available options:
"none": the default ordering in the data is used
"random": a random ordering
"time": ordering accorrding to time (only for space-time models)
"time_random_space": ordering according to time and randomly for all spatial points with the same time points (only for space-time models)
A string specifying the method for choosing inducing points
Available options:
"kmeans++: the k-means++ algorithm
"cover_tree": the cover tree algorithm
"random": random selection from data points
An integer specifying the number of inducing
points / knots for, e.g., a predictive process approximation
A numeric specifying the radius (= "spatial resolution")
for the cover tree algorithm
A string specifying the method used for inverting covariance matrices.
Available options:
"cholesky": Cholesky factorization
"iterative": iterative methods. A combination of conjugate gradient, Lanczos algorithm, and other methods. This is currently only supported for the following cases:
likelihood != "gaussian" and gp_approx == "vecchia" (non-Gaussian likelihoods with a Vecchia-Laplace approximation)
likelihood == "gaussian" and gp_approx == "full_scale_tapering" (Gaussian likelihood with a full-scale tapering approximation)
An integer specifying the seed used for model creation
(e.g., random ordering in Vecchia approximation)
A string specifying the type of Vecchia approximation used for making predictions.
Default value if vecchia_pred_type = NULL: "order_obs_first_cond_obs_only".
Available options:
"order_obs_first_cond_obs_only": Vecchia approximation for the observable process and observed training data is ordered first and the neighbors are only observed training data points
"order_obs_first_cond_all": Vecchia approximation for the observable process and observed training data is ordered first and the neighbors are selected among all points (training + prediction)
"latent_order_obs_first_cond_obs_only": Vecchia approximation for the latent process and observed data is ordered first and neighbors are only observed points
"latent_order_obs_first_cond_all": Vecchia approximation for the latent process and observed data is ordered first and neighbors are selected among all points
"order_pred_first": Vecchia approximation for the observable process and prediction data is ordered first for making predictions. This option is only available for Gaussian likelihoods
an integer specifying the number of neighbors for the Vecchia approximation
for making predictions. Default value if NULL: num_neighbors_pred = 2 * num_neighbors
a numeric specifying the tolerance level for L2 norm of residuals for
checking convergence in conjugate gradient algorithms when being used for prediction
Default value if NULL: 1e-3
an integer specifying the number of samples when simulation
is used for calculating predictive variances
Default value if NULL: 1000
an integer specifying the rank
of the matrix for approximating predictive covariances obtained using the Lanczos algorithm
Default value if NULL: 1000
A vector with elements indicating independent realizations of
random effects / Gaussian processes (same values = same process realization).
The elements of 'cluster_ids' can be integer, double, or character.
A boolean. If TRUE, the data (groups, coordinates, covariate data for random coefficients)
is freed in R after initialization
A vector with response variable data
A matrix with numeric covariate data for the
fixed effects linear regression term (if there is one)
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".
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". 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" or "lbfgs",
'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.
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 likelihood != "gaussian" and gp_approx == "vecchia" or likelihood == "gaussian" and gp_approx == "vecchia_latent":
"vadu" (= 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
"fitc": modified predictive process preconditioner for inverting (B^-1 * D * B^-T + W^-1)
"pivoted_cholesky": (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
"incomplete_cholesky": zero fill-in incomplete (reverse) Cholesky factorization of (B^T * D^-1 * B + W) using the sparsity pattern of B^T * D^-1 * B approx= Sigma^-1
Options for likelihood == "gaussian" and gp_approx == "full_scale_tapering":
"fitc" (= default): modified predictive process preconditioner
"none": no preconditioner
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.
This is discontinued. Use the renamed equivalent argument offset instead
A vector or matrix with elements being group levels
for which predictions are made (if there are grouped random effects in the GPModel)
A vector or matrix with covariate data
for grouped random coefficients (if there are some in the GPModel)
A matrix with prediction coordinates (=features) for
Gaussian process (if there is a GP in the GPModel)
A vector or matrix with covariate data for
Gaussian process random coefficients (if there are some in the GPModel)
A vector with elements indicating the realizations of
random effects / Gaussian processes for which predictions are made
(set to NULL if you have not specified this when creating the GPModel)
A matrix with prediction covariate data for the
fixed effects linear regression term (if there is one in the GPModel)
A boolean. If TRUE, the (posterior)
predictive covariance is calculated in addition to the (posterior) predictive mean
A boolean. If TRUE, the (posterior)
predictive variances are calculated
Discontinued. Use the argument gp_approx instead