GPModel: Create a 'GPModel' object

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

Create a GPModel object

Description

Create a GPModel which contains a Gaussian process and / or mixed effects model with grouped random effects

Usage

GPModel(likelihood = "gaussian", group_data = NULL,
  group_rand_coef_data = NULL, ind_effect_group_rand_coef = NULL,
  drop_intercept_group_rand_effect = NULL, gp_coords = NULL,
  gp_rand_coef_data = NULL, cov_function = "exponential",
  cov_fct_shape = 0.5, gp_approx = "none", cov_fct_taper_range = 1,
  cov_fct_taper_shape = 0, num_neighbors = 20L,
  vecchia_ordering = "random", ind_points_selection = "kmeans++",
  num_ind_points = 500L, cover_tree_radius = 1,
  matrix_inversion_method = "cholesky", seed = 0L, cluster_ids = NULL,
  free_raw_data = FALSE, vecchia_approx = NULL, vecchia_pred_type = NULL,
  num_neighbors_pred = NULL)

Arguments

likelihood	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 Note: other likelihoods could be implemented upon request
group_data	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
group_rand_coef_data	A vector or matrix with numeric covariate data for grouped random coefficients
ind_effect_group_rand_coef	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'
drop_intercept_group_rand_effect	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.
gp_coords	A matrix with numeric coordinates (= inputs / features) for defining Gaussian processes
gp_rand_coef_data	A vector or matrix with numeric covariate data for Gaussian process random coefficients
cov_function	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
cov_fct_shape	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
gp_approx	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
cov_fct_taper_range	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)
cov_fct_taper_shape	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)
num_neighbors	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
vecchia_ordering	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)
ind_points_selection	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
num_ind_points	An integer specifying the number of inducing points / knots for, e.g., a predictive process approximation
cover_tree_radius	A numeric specifying the radius (= "spatial resolution") for the cover tree algorithm
matrix_inversion_method	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)
seed	An integer specifying the seed used for model creation (e.g., random ordering in Vecchia approximation)
cluster_ids	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.
free_raw_data	A boolean. If TRUE, the data (groups, coordinates, covariate data for random coefficients) is freed in R after initialization
vecchia_approx	Discontinued. Use the argument gp_approx instead
vecchia_pred_type	A string specifying the type of Vecchia approximation used for making predictions. This is discontinued here. Use the function 'set_prediction_data' to specify this
num_neighbors_pred	an integer specifying the number of neighbors for making predictions. This is discontinued here. Use the function 'set_prediction_data' to specify this

Value

A GPModel containing ontains a Gaussian process and / or mixed effects model with grouped random effects

Author(s)

Fabio Sigrist

Examples

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

data(GPBoost_data, package = "gpboost")

#--------------------Grouped random effects model: single-level random effect----------------
gp_model <- GPModel(group_data = group_data[,1], likelihood="gaussian")

#--------------------Gaussian process model----------------
gp_model <- GPModel(gp_coords = coords, cov_function = "exponential",
                    likelihood="gaussian")

#--------------------Combine Gaussian process with grouped random effects----------------
gp_model <- GPModel(group_data = group_data,
                    gp_coords = coords, cov_function = "exponential",
                    likelihood="gaussian")

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