admm_MADMMplasso_cpp: Fit the ADMM part of model for a given lambda vale

In MADMMplasso: Multi Variate Multi Response ADMM with Interaction Effects

Fit the ADMM part of model for a given lambda vale

Description

This function fits a multi-response pliable lasso model over a path of regularization values.

Usage

admm_MADMMplasso_cpp(
  beta0,
  theta0,
  beta,
  beta_hat,
  theta,
  rho1,
  X,
  Z,
  max_it,
  W_hat,
  XtY,
  y,
  N,
  e_abs,
  e_rel,
  alpha,
  lambda,
  alph,
  svd_w_tu,
  svd_w_tv,
  svd_w_d,
  C,
  CW,
  gg,
  my_print = TRUE
)

Arguments

beta0	a vector of length ncol(y) of estimated beta_0 coefficients
theta0	matrix of the initial theta_0 coefficients ncol(Z) by ncol(y)
beta	a matrix of the initial beta coefficients ncol(X) by ncol(y)
beta_hat	a matrix of the initial beta and theta coefficients (ncol(X)+ncol(X) by ncol(Z)) by ncol(y)
theta	an array of initial theta coefficients ncol(X) by ncol(Z) by ncol(y)
rho1	the Lagrange variable for the ADMM which is usually included as rho in the MADMMplasso call.
X	n by p matrix of predictors
Z	n by nz matrix of modifying variables. The elements of z may represent quantitative or categorical variables, or a mixture of the two. Categorical variables should be coded by 0-1 dummy variables: for a k-level variable, one can use either k or k-1 dummy variables.
max_it	maximum number of iterations in loop for one lambda during the ADMM optimization. This is usually included in the MADMMplasso call
W_hat	N by (p+(p by nz)) of the main and interaction predictors. This generated internally when MADMMplasso is called or by using the function generate_my_w.
XtY	a matrix formed by multiplying the transpose of X by y.
y	N by D matrix of responses. The X and Z variables are centered in the function. We recommend that X and Z also be standardized before the call
N	nrow(X)
e_abs	absolute error for the ADMM. This is included int the call of MADMMplasso.
e_rel	relative error for the ADMM. This is included int the call of MADMMplasso.
alpha	mixing parameter, usually obtained from the MADMMplasso call. When the goal is to include more interactions, alpha should be very small and vice versa.
lambda	a vector lambda_3 values for the ADMM call with length ncol(y). This is usually calculated in the MADMMplasso call. In our current setting, we use the same the lambda_3 value for all responses.
alph	an overrelaxation parameter in [1, 1.8], usually obtained from the MADMMplasso call.
svd_w_tu	the transpose of the U matrix from the SVD of W_hat
svd_w_tv	the transpose of the V matrix from the SVD of W_hat
svd_w_d	the D matrix from the SVD of W_hat
C	the trained tree
CW	weights for the trained tree The easy way to obtain this is by using the function (tree_parms) which gives a default clustering. However, user decide on a specific structure and then input a tree that follows such structure.
gg	penalty terms for the tree structure for lambda_1 and lambda_2 for the ADMM call.
my_print	Should information form each ADMM iteration be printed along the way? Default TRUE. This prints the dual and primal residuals

Value

predicted values for the ADMM part

MADMMplasso documentation built on April 3, 2025, 10:53 p.m.