RSAVS_Summary_Iteration: Summary the iterations during ADMM algorithm

In fenguoerbian/RSAVS: Robust Subgroup Analysis and Variable Selection

Summary the iterations during ADMM algorithm

Description

This function is designed to summary and improve the resutls during the iteration of ADMM algorithm.

Usage

RSAVS_Summary_Iteration(
  y_vec,
  x_mat,
  beta_vec,
  mu_vec,
  s_vec,
  w_vec,
  loss_type,
  loss_param,
  phi
)

Arguments

y_vec	numerical response vector. n = length(y_vec) is the number of observations.
x_mat	numerical covariate matrix. p = ncol(x_mat) is the number of covariates.
beta_vec	covariate effect vector during the ADMM algorithm.
mu_vec	subgroup effect vector during the ADMM algorithm
s_vec	augmented vector for pair-wise difference of mu_vec in ADMM algorithm.
w_vec	augmented vector for beta_vec in ADMM algorithm.
loss_type	character string indicating type of loss function.
loss_param	numerical vector for necessary parameters in loss function.
phi	a parameter needed in mBIC. It controls how strong mBIC penalizes the complexity of the candidate model.

Details

This function has two purposes:

• Determine and improve beta_vec and mu_vec, if possible.

• Compute BIC.

Since for large scale data set, especially with big number of observations, it's impossible to first save all the variables during the ADMM algorithm over the lam1_length * lam2_length grid points of lambdas, then pick a best solution with mBIC. For s_vec alone, this means we have to save a matrix with n * (n - 1) / 2 rows and lam1_length * lam2_length columns, which is hard for a single computer. Instead, we summarise each iteration during the algorithm. Then there's no need for storing so many data.

In the ADMM algorithm, it will take many iterations to reach a sharp tolerance. But one can stop the algorithm early stage by setting a small max_iter. This is equivalent to setting a loose tolerance. Then the mu_vec and beta_vec will not be close to their augmented counterparts s_vec and w_vec. But these counterparts actually provides the sparsity information during the algorithm, therefore

• w_vec will provide the estimate of covariate effect while beta_vec is just a intermediate variable.

• mu_vec is also the intermediate variable. Improvement is needed like forming a reasonalbe subgroup structure. One possible solution is to utilize s_vec to improve mu_vec. Another is to apply some cluster methods on mu_vec. See RSAVS_Determine_Mu for more details.

Value

a list, containing:

• bic: the bic value.

• mu_vec: the improved mu vector.

• group_num: number of subgroups in the improved mu_vec.

• active_num: number of active covariates in the beta_vec.

fenguoerbian/RSAVS documentation built on Oct. 25, 2024, 3:16 p.m.