CVEK (version 0.1-2)

estimation: Conducting Gaussian Process Regression

Description

Conduct Gaussian process regression based on the estimated ensemble kernel matrix.

Usage

estimation(
  Y,
  X,
  K_list = NULL,
  mode = "loocv",
  strategy = "stack",
  beta_exp = 1,
  lambda = exp(seq(-10, 5)),
  ...
)

Arguments

Y

(matrix, n*1) The vector of response variable.

X

(matrix, n*d_fix) The fixed effect matrix.

K_list

(list of matrices) A nested list of kernel term matrices. The first level corresponds to each base kernel function in kern_func_list, the second level corresponds to each kernel term specified in the formula.

mode

(character) A character string indicating which tuning parameter criteria is to be used.

strategy

(character) A character string indicating which ensemble strategy is to be used.

beta_exp

(numeric/character) A numeric value specifying the parameter when strategy = "exp" ensemble_exp.

lambda

(numeric) A numeric string specifying the range of tuning parameter to be chosen. The lower limit of lambda must be above 0.

...

Additional parameters to pass to estimate_ridge.

Value

lambda

(numeric) The selected tuning parameter based on the estimated ensemble kernel matrix.

beta

(matrix, d_fixed*1) Fixed effect estimates.

alpha

(matrix, n*1) Kernel effect estimates.

K

(matrix, n*n) Estimated ensemble kernel matrix.

u_hat

(vector of length K) A vector of weights of the kernels in the library.

kern_term_effect

(matrix, n*n) Estimated ensemble kernel effect matrix.

base_est

(list) The detailed estimation results of K kernels.

Details

After obtaining the ensemble kernel matrix, we can calculate the output of Gaussian process regression.

See Also

strategy: ensemble