DCADMM_iter_l1 {SILFS}

SILFS-Based Subgroup Identification and Variable Selection Optimized by DC-ADMM under the L1 Distance

Description

This function employs SILFS method and uses the corresponding Difference of Convex functions-Alternating Direction Method of Multipliers (DC-ADMM) algorithm for optimization to identify subgroup structures and conduct variable selection under the L1 Distance.

Usage

DCADMM_iter_l1(
  Y,
  F_hat,
  U_hat,
  r_1,
  r_2,
  r_3,
  lambda_1,
  lambda_2,
  K,
  alpha_init,
  epsilon_1,
  epsilon_2
)

Arguments

Y

The response vector of length n.

F_hat

The estimated factor matrix of size n \times r.

U_hat

The estimated idiosyncratic factors matrix of size n \times p.

r_1

The Lagrangian augmentation parameter for constraints of intercepts.

r_2

The Lagrangian augmentation parameter for constraints of group centers.

r_3

The Lagrangian augmentation parameter for constraints of coefficients.

lambda_1

The tuning parameter for Center-Augmented Regularization.

lambda_2

The tuning parameter for LASSO.

K

The estimated group number.

alpha_init

The initialization of intercept parameter.

epsilon_1

The user-supplied stopping error for outer loop.

epsilon_2

The user-supplied stopping error for inner loop.

Value

A list with the following components:

alpha_curr

The estimated intercept parameter vector of length n.

gamma_curr

The estimated vector of subgroup centers of length K.

theta_curr

The estimated regression coefficient vector, matched with common factor terms, with a dimension of r.

beta_curr

The estimated regression coefficients matched with idiosyncratic factors, with a dimension of p.

Author(s)

Yong He, Liu Dong, Fuxin Wang, Mingjuan Zhang, Wenxin Zhou.

References

He, Y., Liu, D., Wang, F., Zhang, M., Zhou, W., 2024. High-Dimensional Subgroup Identification under Latent Factor Structures.

Examples

n <- 50
p <- 50
r <- 3
K <- 2
alpha <- sample(c(-3,3),n,replace=TRUE,prob=c(1/2,1/2))
beta <- c(rep(1,2),rep(0,48))
B <- matrix((rnorm(p*r,1,1)),p,r)
F_1 <- matrix((rnorm(n*r,0,1)),n,r)
U <- matrix(rnorm(p*n,0,0.1),n,p)
X <- F_1%*%t(B)+U
Y <- alpha + X%*%beta + rnorm(n,0,0.5)
alpha_init <- INIT(Y,F_1,0.1)
DCADMM_iter_l1(Y,F_1,U,0.5,0.5,0.5,0.01,0.05,K,alpha_init,1,0.3)