This function carries out robust subgroup analysis and variable selection simultaneously. It utilizes the cpp core solver and supports different types of loss functions and penalties.
RSAVS_Path(
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 = NULL,
lam2_vec = NULL,
lam1_sort = TRUE,
lam2_sort = TRUE,
min_lam1_ratio = 0.03,
min_lam2_ratio = 0.03,
lam1_max_ncvguard = 100,
lam1_len = 50,
lam2_len = 40,
const_r123 = NULL,
const_abc = rep(1, 3),
initial_values = NULL,
phi = 1,
tol = 0.001,
max_iter = 10,
cd_max_iter = 1,
cd_tol = 0.001,
subgroup_benchmark = FALSE,
update_mu = NULL,
loss_track = FALSE,
diff_update = TRUE,
omp_zsw = c(1, 4, 1),
eigen_pnum = 4,
s_v2 = TRUE,
dry_run = FALSE
)numerical vector of response. n = length(y_vec) is the number of observations.
numerical matrix of covariates. Each row for one observation and
p = ncol(x_mat) is the number of covariates.
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".
numeric vector containing necessary parameters of the corresponding loss function.
The default value is NULL.
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".
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 serve only as placeholder
and will be ignored and overwritten in the actual computation.
numerical vectors of customized lambda vectors.
For lam1_vec, it's preferred to be in the order from small to big.
boolen, whether to force sorting the provided lam1_vec and lam2_vec.
By default, lam1_vec will sort in increasing order while lam2_vec in decreasing order.
the ratio between the minimal and maximal lambda, equals to (minimal lambda) / (maximal lambda). The default value is 0.03.
a safe guard constant for lam1_max when the penalty is nonconvex such as SCAD and MCP.
integers, lengths of the auto-generated lambda vectors.
a length-3 numerical vector, providing the scalars needed in the augmented lagrangian part of the ADMM algorithm
a length-3 numeric vector, providing the scalars to adjust weight
of regression function, penalty for subgroup identification and penalty for
variable selection in the overall objective function. Defaults to c(1, 1, 1).
list of vector, providing initial values for the algorithm.
numerical variable. A parameter needed for mBIC.
numerical, convergence tolerance for the algorithm.
integer, max number of iteration during the algorithm.
integer, max number of iteration during the coordinate descent
update of mu and beta. If set to 0, will use analytical solution(
instead of coordinate descent algorithm) to update mu and beta.
numerical, convergence tolerance for the coordinate descent part
when updating mu and beta.
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.
list of parameters for updating mu_vec in the algorithm into meaningful subgroup structure.
Defaults to NULL, which means there is no update performed. The update of mu_vec is carried out through
RSAVS_Determine_Mu and the necessary parameters in update_mu are:
UseS: a bool variable, whether the s_vec should be used to provide subgroup structure information.
klim: a length-3 integer vector, given the range of number of cluster for considering.
usepam: a bool variable, whether to use pam for clustering.
round_digits: non-negative integer digits, indicating the rounding digits when merging mu_vec
Please refer to RSAVS_Determine_Mu to find out more details about how the algorithm works
boolen, whether to track the value of objective function(loss value) during each iteration.
boolen, whether to update the difference between each iteration. If set to FALSE,
the algorithm will still stop when it reaches max_iter.
a length-three integer vector, defaults to c(1, 4, 1). It represents how many
parallel threads to be used during the update of z, s and w respectively.
integer number, representing the number of Eigen threads for matrix computation, defaults to 4.
boolen, whether to use the updated and faster version during the computation of
s and q2
boolen, whether this is a so-called 'dry-run'. A dry-run will not carry out the real core solver, but only prepares and return the necessary initial values, additional values and solution plane for the core solver.
# 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_Path(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...
#> `initial_values` is missing, use default settings!
#> prepare intermediate variables needed by the algorithm
#> generate pairwise difference matrix
#> compute `beta_lhs`
#> compute `mu_lhs`
#> additional variables prepared!