Robust subgroup analysis and variable selection simultaneously for large scale dataset

Source: R/pre_define_functions.r

This function carries out robust subgroup analysis and variable selection simultaneously. It's implemented in a parallel fashion. It supports different types of loss functions and penalties.

RSAVS_LargeN(
  y_vec,
  x_mat,
  l_type = "L1",
  l_param = NULL,
  p1_type = "S",
  p1_param = c(2, 3.7),
  p2_type = "S",
  p2_param = c(2, 3.7),
  lam1_vec,
  lam2_vec,
  min_lam1_ratio = 0.03,
  min_lam2_ratio = 0.03,
  lam1_len,
  lam2_len,
  const_r123,
  const_abc = rep(1, 3),
  initial_values,
  phi = 1,
  tol = 0.001,
  max_iter = 10,
  cd_max_iter = 1,
  cd_tol = 0.001,
  subgroup_benchmark = FALSE
)

Arguments

y_vec

numerical vector of response. n = length(y_vec) is the number of observations.

x_mat

numerical matrix of covariates. Each row for one observation and p = ncol(x_mat) is the number of covariates.

l_type

character string, type of loss function.

  • "L1": l-1 loss(absolute value loss)

  • "L2": l-2 loss(squared error loss)

  • "Huber": Huber loss. Its parameter is given in l_param.

Default value is "L1".

l_param

numeric vector containing necessary parameters of the corresponding loss function. The default value is NULL.

p1_type, p2_type

a character indicating the penalty types for subgroup identification and variable selection.

  • "S": SCAD

  • "M": MCP

  • "L": Lasso

Default values for both parameters are "S".

p1_param, p2_param

numerical vectors providing necessary parameters for the corresponding penalties.

  • For Lasso, lam = p_param[1]

  • For SCAD and MCP, lam = p_param[1], gamma = p_param[2]

Default values for both parameters are c(2, 3.7). Note: This function searches the whole lam1_vec * lam2_vec grid for the best solution. Hence the lambdas provided in these parameters will be ignored and overwritten.

lam1_vec, lam2_vec

numerical vectors of customized lambda vectors. For lam1_vec, it's preferred to be in the order from small to big.

lam1_len, lam2_len

integers, lengths of the auto-generated lambda vectors.

phi

numerical variable. A parameter needed for mBIC.

tol

numerical, convergence tolerance for the algorithm.

max_iter

integer, max number of iteration during the algorithm.

subgroup_benchmark

bool. Whether this call should be taken as a benchmark of subgroup identification. If TRUE, then the penalty for variable selection will be surpressed to a minimal value.

min_lam_ratio

the ratio between the minimal and maximal lambda, equals to (minimal lambda) / (maximal lambda). The default value is 0.03.

initial_vec

list of vector, providing initial values for the algorithm. mu_initial = initial_vec$mu and beta_initial = initial_vec$beta. Note: Current the function uses auto-generated lambda vectors and the corresponding initial values are all just shrinked to 0. Hence this parameter is ignored.

Examples

# a toy example
# first we generate data
n <- 200    # number of observations
q <- 5    # number of active covariates
p <- 50    # number of total covariates
k <- 2    # number of subgroups

# k subgroup effect, centered at 0
group_center <- seq(from = 0, to = 2 * (k - 1), by = 2) - (k - 1)
# covariate effect vector
beta_true <- c(rep(1, q), rep(0, p - q))
# subgroup effect vector    
alpha_true <- sample(group_center, size = n, replace = TRUE)    
x_mat <- matrix(rnorm(n * p), nrow = n, ncol = p)    # covariate matrix
err_vec <- rnorm(n, sd = 0.1)    # error term
y_vec <- alpha_true + x_mat %*% beta_true + err_vec    # response vector

# a simple analysis using default loss and penalties
res <- RSAVS_LargeN(y_vec = y_vec, x_mat = x_mat, 
                    lam1_len = 50, lam2_len = 40, 
                    phi = 5)
#> `const_r123` is missing. Use default settings!
#> lam1_vec is missing, use default values...
#> lam2_vec is missing, use default values...
#> prepare intermediate variables needed by the algorithm
#> Basic variables initialized.
#> Beta finished.
#> Mu finished.
#> Z finished.
#> S finished.
#> W finished.
#> q1 finished.
#> q2 finished.
#> q3 finished.
#> D started.
#> D finished.
#> beta left finished.
#> mu left finished.

# you can choose different loss and penalties
res_huber <- RSAVS_LargeN(y_vec = y_vec, x_mat = x_mat, 
                          l_type = "Huber", l_param = 1.345,
                          p1_type = "M", p2_type = "L",
                          lam1_len = 40, lam2_len = 30, 
                          phi = 5)
#> `const_r123` is missing. Use default settings!
#> lam1_vec is missing, use default values...
#> lam2_vec is missing, use default values...
#> prepare intermediate variables needed by the algorithm
#> Basic variables initialized.
#> Beta finished.
#> Mu finished.
#> Z finished.
#> S finished.
#> W finished.
#> q1 finished.
#> q2 finished.
#> q3 finished.
#> D started.
#> D finished.
#> beta left finished.
#> mu left finished.
# you can do post-selection estimation by
ind <- res$best_ind    # pick an id of the solution
res2 <- RSAVS_Further_Improve(y_vec = y_vec, x_mat = x_mat, 
                              mu_vec = res$mu_improve_mat[ind, ], 
                              beta_vec = res$w_mat[ind, ])