R/CV_L2E_TF_lasso.R

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

#' Cross validation for L2E trend filtering regression with Lasso penalization
#'
#' \code{CV_L2E_TF_lasso} performs k-fold cross-validation for robust trend filtering regression under the L2 criterion with the Lasso penalty
#'
#' @param y Response vector
#' @param X Design matrix. Default is the identity matrix.
#' @param beta0 Initial vector of regression coefficients, can be omitted
#' @param tau0 Initial precision estimate, can be omitted
#' @param D The fusion matrix
#' @param lambdaSeq A decreasing sequence of tuning parameter lambda, can be omitted
#' @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 calculate the objective value
#' @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
#' @importFrom stats mad
#' @importFrom stats median
#' @export
#' @examples
#' ## Completes in 30 seconds
#'
#' set.seed(12345)
#' n <- 100
#' x <- 1:n
#' f <- matrix(rep(c(-2,5,0,-10), each=n/4), ncol=1)
#' y <- y0 <- f + rnorm(length(f))
#'
#' ## Clean Data
#' plot(x, y, pch=16, cex.lab=1.5, cex.axis=1.5, cex.sub=1.5, col='gray')
#' lines(x, f, lwd=3)
#'
#' D <- myGetDkn(1, n)
#' lambda <- 10^seq(-1, -2, length.out=20)
#' # (not run)
#' # cv <- CV_L2E_TF_lasso(y=y0, D=D, lambdaSeq=lambda, nfolds=2, seed=1234)
#' # (lambda_min <- cv$lambda.min)
#'
#' # sol <- L2E_TF_lasso(y=y0, D=D, lambdaSeq=lambda_min)
#'
#' # plot(x, y, pch=16, cex.lab=1.5, cex.axis=1.5, cex.sub=1.5, col='gray')
#' # lines(x, f, lwd=3)
#' # lines(x, sol$Beta, col='blue', lwd=3)
#'
#' ## Contaminated Data
#' ix <- sample(1:n, 10)
#' y[ix] <- y0[ix] + 2
#'
#' plot(x, y, pch=16, cex.lab=1.5, cex.axis=1.5, cex.sub=1.5, col='gray')
#' lines(x, f, lwd=3)
#'
#' # (not run)
#' # cv <- CV_L2E_TF_lasso(y=y, D=D, lambdaSeq=lambda, nfolds=2, seed=1234)
#' # (lambda_min <- cv$lambda.min)
#'
#' # sol <- L2E_TF_lasso(y=y, D=D, lambdaSeq=lambda_min)
#'
#' # plot(x, y, pch=16, cex.lab=1.5, cex.axis=1.5, cex.sub=1.5, col='gray')
#' # lines(x, f, lwd=3)
#' # lines(x, sol$Beta, col='blue', lwd=3)
#'
CV_L2E_TF_lasso <- function(y,X,beta0,tau0,D,lambdaSeq,nfolds=5,seed=1234,method="median",
                            max_iter=1e2,tol=1e-4,trace=TRUE) {


  if(missing(X)){
    X <- diag(nrow = length(y))  # initial X
  }

  if(missing(beta0)){
    beta0 <-  rep(mean(y), ncol(X))  # initial beta
  }

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

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

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

  # 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$beta0 <- beta0
  cv.args$tau0 <- tau0
  cv.args$D <- D
  cv.args$lambdaSeq <- lambdaSeq
  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_TF_lasso(i, y, X, fold, cv.args, method=method)
    Loss[i, ] <- res
  }

  # Return
  cve <- apply(Loss, 2, median)  ### use median instead of mean to account for the possibility of outlieirs in the hold-out fold
  cvse <- apply(Loss, 2, sd)/sqrt(nfolds)
  min <- which.min(cve)


  # 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_TF_lasso <- 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_TF_lasso", 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)
}