estimation: Conducting Gaussian Process Regression

In IrisTeng/CVEK: Cross-Validated Kernel Ensemble

Description

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

Usage

estimation(Y, X1, X2, kern_list, mode = "loocv", strategy = "erm",
  beta = 1, lambda = exp(seq(-5, 5)))

Arguments

Y	(vector of length n) Reponses of the dataframe.
X1	(dataframe, n*p1) The first type of factor in the dataframe (could contains several subfactors).
X2	(dataframe, n*p2) The second type of factor in the dataframe (could contains several subfactors).
kern_list	(list of length K) A list of kernel functions given by user.
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	(numeric/character) A numeric value specifying the parameter when strategy = "exp" ensemble_exp.
lambda	(numeric) A numeric string specifying the range of noise to be chosen. The lower limit of lambda must be above 0.

Details

After obtaining the ensemble kernel matrix, we can calculate the outpur of gaussian process regression, the solution is given by

\hat{β}=[1^T(K+λ I)^{-1}1]^{-1}1^T(K+λ I)^{-1}y

\hat{α}=(K+λ I)^{-1}(y-\hat{β}1)

where β=intercept.

Value

lam	(numeric) The selected tuning parameter based on the estimated ensemble kernel matrix.
intercept	(numeric) Estimated bias of the model.
alpha	(vector of length n) Estimated coefficients of the estimated ensemble kernel matrix.
K	(matrix, n*n) Estimated ensemble kernel matrix.
u_hat	(vector of length K) A vector of weights of the kernels in the library.

Author(s)

Wenying Deng

See Also

strategy: ensemble

Examples

estimation(Y, X1, X2, kern_list, mode = "loocv", strategy = "erm",
beta = 1, lambda = exp(seq(-5, 5)))

IrisTeng/CVEK documentation built on May 31, 2019, 4:50 p.m.