adass.fr_eaass: Evolutionary algorithm for the adaptive smoothing spline estimator (EAASS).

Description

EAASS algorithm to choose the tuning parameters for the AdaSS estimator (Centofanti et al., 2020).

Usage

adass.fr_eaass(
  Y_fd,
  X_fd,
  basis_s,
  basis_t,
  beta_ders = NULL,
  beta_dert = NULL,
  grid_eval_ders = NULL,
  grid_eval_dert = NULL,
  rand_search_par = list(c(-4, 4), c(-4, 4), c(0, 1, 5, 10, 15), c(0, 1, 2, 3, 4), c(0,
    1, 5, 10, 15), c(0, 1, 2, 3, 4)),
  popul_size = 12,
  iter_num = 10,
  r = 0.2,
  pert_vec = c(0.8, 1.2),
  X_fd_test = NULL,
  Y_fd_test = NULL,
  progress = TRUE,
  ncores = 1,
  K = 10
)

Value

A list containing the following arguments:

tun_par_opt: Vector of optimal tuning parameters.
CV: Estimated prediction errors.
CV_sd: Standard errors of the estimated prediction errors.
comb_list: The combinations of tuning parameters explored.
Y_fd: The response functions.
X_fd: The covariate functions.

Arguments

Y_fd: An object of class fd corresponding to the response functions.
X_fd: An object of class fd corresponding to the covariate functions.
basis_s: B-splines basis along the s-direction of class basisfd.
basis_t: B-splines basis along the t-direction of class basisfd.
beta_ders: Initial estimate of the partial derivative of the coefficient function along the s-direction. Either a matrix or a class basisfd object. If NULL no adaptive penalty is used along the s-direction.
beta_dert: Initial estimate of the partial derivative of the coefficient function along the t-direction. Either a matrix or a class basisfd object. If NULL no adaptive penalty is used along the t-direction.
grid_eval_ders: Grid of evaluation of the partial derivatives along the s-direction.
grid_eval_dert: Grid of evaluation of the partial derivatives along the t-direction.
rand_search_par: List containing the initial population ranges for the tuning parameters.
popul_size: Initial population size.
iter_num: Algorithm iterations.
r: Truncation parameter in the exploitation phase.
pert_vec: Perturbation parameters in the exploration phase.
X_fd_test: Test set covariate functions. Default is NULL. If X_fd_test and Y_fd_test are both provided the prediction error on the test set is used as performance metric in place of the cross-validation prediction error.
Y_fd_test: Test set response functions. Default is NULL. If X_fd_test and Y_fd_test are both provided the prediction error on the test set is used as performance metric in place of the cross-validation prediction error.
progress: If TRUE a progress bar is printed. Default is TRUE.
ncores: If ncores>1, then parallel computing is used, with ncores cores. Default is 1.
K: Number of folds. Default is 10.

References

Centofanti, F., Lepore, A., Menafoglio, A., Palumbo, B., Vantini, S. (2023). Adaptive Smoothing Spline Estimator for the Function-on-Function Linear Regression Model. Computational Statistics 38(1), 191–216.

Examples

Run this code

library(adass)
data<-simulate_data("Scenario HAT",n_obs=100)
X_fd=data$X_fd
Y_fd=data$Y_fd
basis_s <- fda::create.bspline.basis(c(0,1),nbasis = 5,norder = 4)
basis_t <- fda::create.bspline.basis(c(0,1),nbasis = 5,norder = 4)
mod_smooth <-adass.fr(Y_fd,X_fd,basis_s = basis_s,basis_t = basis_t,tun_par=c(10^-6,10^-6,0,0,0,0))
grid_s<-seq(0,1,length.out = 5)
grid_t<-seq(0,1,length.out = 5)
beta_der_eval_s<-fda::eval.bifd(grid_s,grid_t,mod_smooth$Beta_hat_fd,sLfdobj = 2)
beta_der_eval_t<-fda::eval.bifd(grid_s,grid_t,mod_smooth$Beta_hat_fd,tLfdobj = 2)
mod_adsm<-adass.fr_eaass(Y_fd,X_fd,basis_s,basis_t,
                        beta_ders=beta_der_eval_s, beta_dert=beta_der_eval_t,
                        rand_search_par=list(c(-8,4),c(-8,4),c(0,0.1),c(0,4),c(0,0.1),c(0,4)),
                        grid_eval_ders=grid_s, grid_eval_dert=grid_t,
                        popul_size = 1,ncores=1,iter_num=1)