R/CovEst.soft.R

In kyoustat/CovTools: Statistical Tools for Covariance Analysis

#  Original name : Donoho95
#' Covariance Estimation via Soft Thresholding
#'
#' Soft Thresholding method for covariance estimation takes off-diagonal elements \eqn{z} of sample covariance matrix and applies
#' \deqn{h_{\tau}(z) = \textrm{sgn}(z)(|z|-\tau)_{+}}
#' where \eqn{\textrm{sgn}(z)} is a sign of the value \eqn{z}, and \eqn{(x)_+ = \textrm{max}(x,0)}. If \code{thr} is rather a vector of regularization parameters, it applies
#' cross-validation scheme to select an optimal value.
#'
#' @param X an \eqn{(n\times p)} matrix where each row is an observation.
#' @param thr user-defined threshold value. If it is a vector of regularization values, it automatically selects one that minimizes cross validation risk.
#' @param nCV the number of repetitions for 2-fold random cross validations for each threshold value.
#' @param parallel a logical; \code{TRUE} to use half of available cores, \code{FALSE} to do every computation sequentially.
#'
#' @return a named list containing: \describe{
#' \item{S}{a \eqn{(p\times p)} covariance matrix estimate.}
#' \item{CV}{a dataframe containing vector of tested threshold values(\code{thr}) and corresponding cross validation scores(\code{CVscore}).}
#' }
#'
#' @examples
#' ## generate data from multivariate normal with Identity covariance.
#' pdim <- 5
#' data <- matrix(rnorm(10*pdim), ncol=pdim)
#'
#' ## apply 4 different schemes
#' #  mthr is a vector of regularization parameters to be tested
#' mthr <- exp(seq(from=log(0.1),to=log(10),length.out=10))
#'
#' out1 <- CovEst.soft(data, thr=0.1)  # threshold value 0.1
#' out2 <- CovEst.soft(data, thr=1)    # threshold value 1
#' out3 <- CovEst.soft(data, thr=10)   # threshold value 10
#' out4 <- CovEst.soft(data, thr=mthr) # automatic threshold checking
#'
#' ## visualize 4 estimated matrices
#' gcol <- gray((0:100)/100)
#' opar <- par(no.readonly=TRUE)
#' par(mfrow=c(2,2), pty="s")
#' image(out1$S[,pdim:1], col=gcol, main="thr=0.1")
#' image(out2$S[,pdim:1], col=gcol, main="thr=1")
#' image(out3$S[,pdim:1], col=gcol, main="thr=10")
#' image(out4$S[,pdim:1], col=gcol, main="automatic")
#' par(opar)
#'
#' @references
#' \insertRef{antoniadis_regularization_2001}{CovTools}
#'
#' \insertRef{donoho_wavelet_1995}{CovTools}
#'
#' @rdname CovEst.soft
#' @export
CovEst.soft <- function(X, thr=0.5, nCV=10, parallel=FALSE){
  #-----------------------------------------------------
  ## PREPROCESSING
  fname    = "CovEst.soft"
  pnameTHR = "'thr'"
  pnamenCV = "'nCV"
  pnamenthrs = "'nthrs'"
  #   1. data matrix
  checker1 = invisible_datamatrix(X, fname)
  #   2. thr
  if (length(as.vector(thr))==1){
    checker3 = invisible_PosReal(thr, fname, pnameTHR)
    CV = FALSE
  } else { # vector threshold value case
    nthrs = length(thr)
    for (i in 1:nthrs){
      checker3 = invisible_PosReal(thr[i], fname, pnameTHR)
    }
    CV = TRUE
  }
  #   4. nCV
  if (CV==TRUE){
    nCV = as.integer(nCV)
    checker4 = invisible_PosIntMM(nCV, fname, pnamenCV, 1, nrow(X))
  }
  #   5. parallel
  if (!parallel){
    nCore = 1
  } else {
    nCore = max(round(detectCores()/2),1)
  }

  #-----------------------------------------------------
  ## MAIN COMPUTATION
  if (CV==FALSE){
    output = thr1.once(X,thr,func_soft)
  } else {
    output = thr1.multiple(X,nCV,nCore,func_soft_givenS,thr)
  }

  #-----------------------------------------------------
  ## RETURN OUTPUT
  return(output)
}







# Auxiliary Functions for Soft Thresholding -------------------------------
#' @keywords internal
#' @noRd
func_soft <- function(X, thr){
  S      = cov(X)
  diagS  = diag(S)
  output = array(0,dim(S))

  idxPos = which(S>abs(thr))
  idxNeg = which(S<(-abs(thr)))

  output[idxPos] = S[idxPos]-thr
  output[idxNeg] = S[idxNeg]+thr
  diag(output)   = diagS
  return(output)
}
#' @keywords internal
#' @noRd
func_soft_givenS <- function(S, thr){
  diagS  = diag(S)
  output = array(0,dim(S))

  idxPos = which(S>abs(thr))
  idxNeg = which(S<(-abs(thr)))

  output[idxPos] = S[idxPos]-thr
  output[idxNeg] = S[idxNeg]+thr
  diag(output)   = diagS
  return(output)
}