View source: R/gp.functions6.R
gpr | R Documentation |
Gaussian process regression for a single or multiple independent realisations.
gpr( response, input, Cov = "pow.ex", m = NULL, hyper = NULL, NewHyper = NULL, meanModel = 0, mu = NULL, gamma = 2, nu = 1.5, useGradient = T, iter.max = 100, rel.tol = 8e-10, trace = 0, nInitCandidates = 1000 )
response |
Response data. It should be a matrix, where each column is a realisation. It can be a vector if there is only one realisation. |
input |
Input covariates. It must be either a matrix, where each column represents a covariate, or a vector if there is only one covariate. |
Cov |
Covariance function(s) to use. Options are: 'linear', 'pow.ex', 'rat.qu', and 'matern'. Default to 'power.ex'. |
m |
If Subset of Data is to be used, m denotes the subset size and cannot be larger than the total sample size. Default to NULL. |
hyper |
The hyperparameters. Default to NULL. If not NULL, then it must be a list with appropriate names. |
NewHyper |
Vector of names of the new hyperparameters of the customized kernel function. These names must have the format: xxxxxx.x, i.e. '6 digit' followed by 'a dot' followed by '1 digit'. This is required for both 'hyper' and 'NewHyper' |
meanModel |
Type of mean function. It can be
Default to 0. If argument 'mu' is specified, then 'meanModel' will be set to 'userDefined'. |
mu |
Mean function specified by the user. It must be a vector. Its length must be the same as the sample size, that is, nrow(response). |
gamma |
Power parameter used in powered exponential kernel function. It must be 0<gamma<=2. |
nu |
Smoothness parameter of the Matern class. It must be a positive value. |
useGradient |
Logical. If TRUE, first derivatives will be used in the optimization. |
iter.max |
Maximum number of iterations allowed. Default to 100. If 'rel.tol' is reduced, then the number of iterations needed will be less. |
rel.tol |
Relative convergence tolerance. Default to 8e-10. Smaller rel.tol means higher accuracy and more time to converge. |
trace |
The value of the objective function and the parameters is printed every trace'th iteration. Defaults to 0 which indicates no trace information is to be printed. |
nInitCandidates |
Number of initial hyperparameter vectors. The optimization starts with the best. |
The most important function of the package. It fits the GPR model and stores everything necessary for prediction. The optimization used in the function is 'nlminb'. The names for the hyperparameters should be: "linear.a" for linear covariance function, "pow.ex.w", "pow.ex.v" for power exponential, "rat.qu.s", "rat.qu.a" for rational quadratic, "matern.w", "matern.v" for Matern, "vv" for variance of Gaussian white noise. All hyperparameters should be in one list.
A list containing:
Hyperparameters vector estimated from training data
Variance of the estimated hyperparameters
Fitted values for the training data
Standard deviation of the fitted values for the training data
Training covariates
Training response
Original training response
Original training covariates
Index vector identifying which observations were selected if Subset of Data was used.
Covariance function type
Parameter used in powered exponential covariance function
Parameter used in Matern covariance function
Covariance matrix
Mean function
Mean model used
'lm' object if mean is a linear regression. NULL otherwise.
An integer. 0 means converge; 1 otherwise.
Starting point of the hyperparameters vector.
Shi, J. Q., and Choi, T. (2011), “Gaussian Process Regression Analysis for Functional Data”, CRC Press.
## See examples in vignettes: # vignette("gpr_ex1", package = "GPFDA") # vignette("gpr_ex2", package = "GPFDA") # vignette("co2", package = "GPFDA")
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