R/CV_L2E_sparse_ncv.R

In jocelynchi/L2E-package-demo: Robust Structured Regression via the L2 Criterion

#' Cross validation for L2E sparse regression with existing penalization methods
#'
#' \code{CV_L2E_sparse_ncv} performs k-fold cross-validation for robust sparse regression under the L2 criterion.
#'  Available penalties include lasso, MCP and SCAD.
#'
#' @param y Response vector
#' @param X Design matrix
#' @param beta0 Initial vector of regression coefficients, can be omitted
#' @param tau0 Initial precision estimate, can be omitted
#' @param lambdaSeq A decreasing sequence of tuning parameter lambda, can be omitted
#' @param penalty Available penalties include lasso, MCP and SCAD.
#' @param nfolds The number of cross-validation folds. Default is 5.
#' @param seed Users can set the seed of the random number generator to obtain reproducible results.
#' @param method Median or mean to compute the objective
#' @param max_iter Maximum number of iterations
#' @param tol Relative tolerance
#' @param trace Whether to trace the progress of the cross-validation
#' @return Returns a list object containing the mean and standard error of the cross-validation error -- CVE and CVSE -- for each value of k (vectors),
#' the index of the lambda with the minimum CVE and the lambda value itself (scalars),
#' the index of the lambda value with the 1SE CVE and the lambda value itself (scalars),
#' the sequence of lambda used in the regression (vector), and
#' a vector listing which fold each element of y was assigned to
#' @export
#' @examples
#' ## Completes in 20 seconds
#'
#' set.seed(12345)
#' n <- 100
#' tau <- 1
#' f <- matrix(c(rep(2,5), rep(0,45)), ncol = 1)
#' X <- X0 <- matrix(rnorm(n*50), nrow = n)
#' y <- y0 <- X0 %*% f + (1/tau)*rnorm(n)
#'
#' ## Clean Data
#' lambda <- 10^seq(-1, -2, length.out=20)
#' # (not run)
#' # cv <- CV_L2E_sparse_ncv(y=y, X=X, lambdaSeq=lambda, penalty="SCAD", seed=1234, nfolds=2)
#' # (lambda_min <- cv$lambda.min)
#'
#' # sol <- L2E_sparse_ncv(y=y, X=X, lambdaSeq=lambda_min, penalty="SCAD")
#' # r <- y - X %*% sol$Beta
#' # ix <- which(abs(r) > 3/sol$Tau)
#' # l2e_fit <- X %*% sol$Beta
#'
#' # plot(y, l2e_fit, ylab='Predicted values', pch=16, cex=0.8)
#' # points(y[ix], l2e_fit[ix], pch=16, col='blue', cex=0.8)
#'
#' ## Contaminated Data
#' i <- 1:5
#' y[i] <- 2 + y0[i]
#' X[i,] <- 2 + X0[i,]
#'
#' # (not run)
#' # cv <- CV_L2E_sparse_ncv(y=y, X=X, lambdaSeq=lambda, penalty="SCAD", seed=1234, nfolds=2)
#' # (lambda_min <- cv$lambda.min)
#'
#' # sol <- L2E_sparse_ncv(y=y, X=X, lambdaSeq=lambda_min, penalty="SCAD")
#' # r <- y - X %*% sol$Beta
#' # ix <- which(abs(r) > 3/sol$Tau)
#' # l2e_fit <- X %*% sol$Beta
#'
#' # plot(y, l2e_fit, ylab='Predicted values', pch=16, cex=0.8)
#' # points(y[ix], l2e_fit[ix], pch=16, col='blue', cex=0.8)
#'
CV_L2E_sparse_ncv <- function(y, X, beta0, tau0, lambdaSeq,  penalty="MCP", nfolds=5, seed=1234, method="median",
                          max_iter=1e2, tol=1e-4, trace=TRUE) {


  if(missing(lambdaSeq)){
    lambdaSeq <- 10^seq(1, -4, length.out = 20)  # set a sequence of lambda
  }

  if(missing(beta0)){
    beta0 <- double(ncol(X))  # initial beta
  }

  if(missing(tau0)){
    tau0 <- 1/mad(y)  # initial tau
  }

  if (tau0 <= 0) stop("Entered non-positive tau0")


  # Set up folds
  if (!missing(seed)) set.seed(seed)
  n <- length(y)
  fold <- sample(1:n %% nfolds)
  fold[fold==0] <- nfolds


  # Do cross-validation

  cv.args <- list()
  cv.args$b <- beta0
  cv.args$tau <- tau0
  cv.args$lambdaSeq <- lambdaSeq
  cv.args$penalty <- penalty
  cv.args$max_iter <- max_iter
  cv.args$tol <- tol
  cv.args$Show.Time <- FALSE


  Loss <- matrix(0, nrow = nfolds, ncol = length(lambdaSeq))
  for (i in 1:nfolds) {
    if (trace) cat("Starting CV fold #", i, sep="","\n")
    res <- cv_fold_l2e_ncv(i, y, X, fold, cv.args, method=method)
    Loss[i, ] <- res
  }

  # Return
  cve <- apply(Loss, 2, mean)
  cvse <- apply(Loss, 2, sd)/sqrt(nfolds)
  min <- which.min(round(cve,8))


  # find the lambda.1se
  for (i in min:1) {
    if(cve[i]>cve[min]+cvse[min])
      break
  }

  if(min==1){
    lambda.1se <- lambdaSeq[1]
    min_1se <- 1
  }else{
    lambda.1se <- lambdaSeq[i+1]
    min_1se <- i+1
  }



  return(list(cve=cve, cvse=cvse, min=min, lambda.min=lambdaSeq[min], min_1se=min_1se, lambda.1se=lambda.1se,
              lambdaSeq=lambdaSeq,  fold=fold))

}





cv_fold_l2e_ncv <- function(i, y, X, fold, cv.args, method="median") {
  cv.args$y <- y[fold!=i]
  cv.args$X <- X[fold!=i, , drop=FALSE]
  fit.i <- do.call("L2E_sparse_ncv", cv.args)

  # data in hold-out
  y_out <- y[fold==i]
  X_out <- X[fold==i, , drop=FALSE]


  L <- length(fit.i$lambdaSeq)
  loss <- double(L)

  for (l in 1:L) {
    bhat <- fit.i$Beta[, l]  # get the estimated beta with the l-th k
    Xbeta <- X_out %*% bhat
    r <- y_out - Xbeta
    tauhat <- fit.i$Tau[l]

    loss[l] <- objective_tau(tau = tauhat, r = r, method=method) ### use median instead of mean to account for outliers
  }

  return(loss)
}