estimation_beta: FLAME for the Function-on-Scalar regression coefficients.

In ardeeshany/FLAME: FLAME for high-dimensional Function-on-Scalar regression problems

Description

This function computes FLAME for the Function-on-Scalar regression problem, returning the significant parameters and the estimated coefficients in the kernel basis.

Usage

estimation_beta(X, Y, eigenval, NoI, thres, number_non_zeros, ratio_lambda,
  number_lambda, proportion_training_set, verbose = FALSE)

Arguments

X	matrix. N \times I design matrix. It has standardized columns.
Y	matrix. J \times N matrix containing the coefficients of the projection of the N response functions on the kernel basis. In particular column n contains the basis projection of y_n.
eigenval	vector. J-length vector containing the eigenvalues of the kernel.
NoI	scalar. integer, maximum number of iterations in the Coordinate-Descent loop.
thres	scalar. tolerance on the K-norm of the increment of the estimation to stop the Coordinate-Descent loop
number_non_zeros	scalar. integer, threshold on the number of non zeros parameters to be detected. It is the kill switch parameter presented in the Vignette.
ratio_lambda	scalar. ratio to compute the minimum value of lambda. The maximum λ_{\max} is computed as the minimum value which makes all the coefficients equal to zero. The minimum is the product ratio_lambda\times λ_{\max}.
number_lambda	scalar. integer, length of the grid for the λ parameter.
proportion_training_set	scalar. value in (0,1), the proportion for the training set for the Cross Validation.
verbose	bool. If TRUE the progression of the algorithm in the adaptive and non adaptive step is shown. If FALSE no output is shown. Default is FALSE.

Value

list containing:

• beta matrix. J \times I matrix of the final estimated coefficients in the kernel basis.

• beta_no_adaptive matrix J \times I matrix of the coefficients estimated at the end of the non-adaptive step.

• predictors vector of the indices of the non-zero estimated predictors.

• predictors_no_adaptive vector of the indices of the non-zeros predictor estimated after the non-adaptive step.

Examples

## Not run: 
data(simulation)
data(SobolevKernel)
I0 <- dim(B_true)[2]
time <- proc.time()
FLAME_estimation <- estimation_beta(X = X,
                                 Y = Y_matrix,
                                 eigenval = eigenval,
                                 NoI = 10,
                                 thres = 0.1,
                                 number_non_zeros = I0*2,
                                 ratio_lambda = 0.01,
                                 number_lambda = 100,
                                 proportion_training_set = 0.75,
                                 verbose = FALSE)
duration <- proc.time()-time
duration
names(FLAME_estimation)

## End(Not run)

ardeeshany/FLAME documentation built on May 14, 2019, 8:41 a.m.