estimation {CVEK}

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.

Details

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

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.

Author(s)

Wenying Deng

See Also

strategy: ensemble