documentation for ElasticQR

Author: yixuan

R/elasticqr.R

@@ -1,5 +1,42 @@
+##' Solving Elastic Net Regularized Quantile Regression
+##'
+##' @description
+##' This function solves the elastic net regularized quantile regression
+##' (ElasticQR) of the following form:
+##' \deqn{
+##' \min_{\beta}\ \frac{1}{n}\sum_{i=1}^n \rho_\kappa(y_i-x_i^T\beta_{1:d}-\beta_{d+1})+
+##' \lambda_1\Vert\beta\Vert_1 + \frac{\lambda_2}{2}\Vert\beta\Vert_2^2
+##' }
+##' where \eqn{\rho_\kappa(u)=u\cdot(\kappa-I(u<0))} is the check loss,
+##' \eqn{\beta\in\mathbb{R}^{d+1}} is a length-\eqn{(d+1)} vector,
+##' \eqn{x_i\in\mathbb{R}^d} is the feature vector for the \eqn{i}-th observation,
+##' \eqn{y_i\in\mathbb{R}} is the \eqn{i}-th response variable value,
+##' and \eqn{\lambda_1,\lambda_2>0} are weights of lasso and ridge penalties,
+##' respectively.
+##'
+##' @param x          The data matrix \eqn{X=(x_1,\ldots,x_n)^T} of size
+##'                   \eqn{n\times d}, representing \eqn{n} observations
+##'                   and \eqn{d} features.
+##' @param y          The length-\eqn{n} response vector.
+##' @param kappa      Parameter of the check loss.
+##' @param lam1,lam2  Weights of lasso and ridge penalties, respectively.
+##' @param max_iter   Maximum number of iterations.
+##' @param tol        Tolerance parameter for convergence test.
+##' @param shrink     Whether to use the shrinkage algorithm.
+##' @param verbose    Level of verbosity.
+##'
+##' @return A list of the following components:
+##' \item{beta}{Optimized value of the \eqn{\beta} vector.}
+##' \item{xi,Lambda,Gamma}{Values of dual variables.}
+##' \item{niter}{Number of iterations used.}
+##' \item{dual_objfns}{Dual objective function values during the optimization process.}
+##'
+##' @author Yixuan Qiu \url{https://statr.me}
+##'
+##'         Ben Dai \url{https://bendai.org}
+##'
 elasticqr = function(x, y, kappa = 0.5, lam1 = 0.1, lam2 = 0.1,
-    max_iter = 1000, tol = 1e-5, verbose = 0)
+    max_iter = 1000, tol = 1e-5, shrink = TRUE, verbose = 0)
 {
     n = nrow(x)
     d = ncol(x)
@@ -19,6 +56,6 @@ elasticqr = function(x, y, kappa = 0.5, lam1 = 0.1, lam2 = 0.1,
     Vmat = rbind(Vr1, Vr2, Vr34)
 
     res = rehline(Xmat, Umat, Vmat, max_iter = max_iter,
-                  tol = tol, verbose = verbose)
+                  tol = tol, shrink = shrink, verbose = verbose)
     res$beta
 }