AFSSEN: AFSSEN

In ardeeshany/AFSSEN: Adaptive Function on Scalar Elastic Net

AFSSEN

Description

It computes important variables and produce smooth estimates of their parameters in a function-on-scalar linear model with sub-Gaussian errors and high-dimensional predictors.

Usage

AFSSEN(X, Y, T_domain = seq(0, 1, length = 50),
  type_kernel = "exponential", param_kernel = 8, thres = 0.02,
  number_non_zeros = 20, ratio_lambda_H = 0.01,
  number_lambda_H = 100, num_lambda_H_NONad = 50,
  lambda_H = numeric(), lambda_K, early_CV = 0,
  early_CV_thres = 0.001, max_ite_nadp = 10, max_ite_adp = 30,
  max_ite_final = 50, target_inc = 1, proportion_training_set = 0.75,
  verbose = FALSE, fold_ad = 10)

Arguments

X	matrix. N by I design matrix. It has standardized columns.
Y	matrix. N by m matrix of pointwise observations.
T_domain	vector. Time domain for evaluation of Y and generating kernel. Default is T_domain = seq(0,1,m=50)
type_kernel	string. three possible choices are implemented. gaussian, Defualt is "exponential". exponential, sobolev.
param_kernel	scalar. Value of the characteristic smoothing parameter of the kernel. It is the σ parameter of the Gaussian and the Exponential kernel, as introduced the σ parameter of the Sobolev. Defualt is 8.
thres	scalar. Stopping criteria: beta increment threshold || β^{T} - β^(T-1) ||_{H} < thres Defualt is 0.02.
number_non_zeros	scalar. Stopping Criteria: Kill switch; number of nonzero predictors Defualt is 20.
ratio_lambda_H	scalar. λ_{Hmax}/λ_{Hmin} Defualt is 0.01.
number_lambda_H	scalar. Generate the number of log-equally spaced λ_{H} in [λ_{Hmin},λ_{Hmax}]. Defualt is 100.
num_lambda_H_NONad	scalar. Number of λ_H in non-adaptive step Defualt is 50.
lambda_H	vector. You have option to insert directly a vector of λ_H. Defualt is numeric().
lambda_K	vector. Vector of λ_{K}.
early_CV	binary. 0 or 1 : applying the early_CV_thres stopping criteria or not. Defualt is 0.
early_CV_thres	scalar. Stopping Criteria: Breaking point in CV plot. |CV(h-1,k)-CV(h,k)| / |CV(h-1,k)| < early_CV_thres Defualt is 0.001.
max_ite_nadp	scalar. Stopping Criteria: Maximum iteration of coordinate descent algorithm in non-adaptive step Defualt is 10.
max_ite_adp	scalar. Stopping Criteria: Maximum iteration of coordinate descent algorithm in adaptive step Defualt is 30.
max_ite_final	scalar. Stopping Criteria: Maximum iteration of coordinate descent algorithm in final step Defualt is 50.
target_inc	binary. Stopping Criteria: 0 or 1 : if target function is increased, stop Defualt is 1.
proportion_training_set	scalar. value in (0,1), the proportion for the training set for the Cross Validation in non-adaptive step Defualt is 0.75.
fold_ad	scalar. Number of fold for using CV in adaptive steps to find optimum λ_{H} and λ_{K} and then the coefficients estimation. Defualt is 10.

Value

list containing:

• beta : matrix. final estimation of coefficients.

• beta_no_adaptive : matrix. estimation of coefficients after non-adaptive step.

• predictors : vector. final significant predictors.

• predictors_no_adaptive : vector. significant predictors after non-adaptive step.

• lambda_H_opt : scalar. optimum λ_{H}

• lambda_K_opt : scalar. optimum λ_{K}

Examples

## Not run: 
data(simulation)
data(SobolevKernel)
time <- proc.time()
FLAME_estimation <- FLAME()
duration <- proc.time()-time
duration
names(FLAME_estimation)

## End(Not run)

ardeeshany/AFSSEN documentation built on Aug. 28, 2022, 2:22 p.m.