R/iCorShrink2Data.R

In kkdey/CorShrink: Adaptive Shrinkage of Correlation and Covariance Matrices

#' @title Adaptive regularized GLASSO of partial correlations from a data matrix with missing data
#' @description Performs an adaptove regularized GLASSO of partial correlations from a data matrix with missing data
#' using the Fisher Z-score formulation
#'
#' @param data_with_missing The samples by features data matrix. May contain NA values.
#' @param alpha The tuning parameter
#' @param expo The exponent on the scaling used in the adaptive regularization of tuning parameter
#' @param shift The shift in the scaling used in adaptive regularization of tuning parameter
#' @param lambda The weight on the constraint for sample size bias
#' @param max_iter The maximum number of iterations for the adaptive GLASSO run.
#' @param epsilon The tolerance level for the relative error specifying when to stop
#'
#' @examples
#' data("sample_by_feature_data")
#' out = iCorShrink2Data(sample_by_feature_data, alpha = 0.1, max_iter = 3)
#' corrplot::corrplot(as.matrix(out), diag = FALSE,
#'         col = colorRampPalette(c("blue", "white", "red"))(200),
#'         tl.pos = "td", tl.cex = 0.4, tl.col = "black",
#'         rect.col = "white",na.label.col = "white",
#'         method = "color", type = "upper")
#'
#' @keywords box shrinkage, correlation
#' @import CVXR
#' @importFrom corrplot corrplot
#' @importFrom stats cov cor sd cov2cor
#' @export

iCorShrink2Data <- function(data_with_missing,
                            alpha,
                            expo = 0.05,
                            shift = 0.01,
                            lambda = 0.8,
                            max_iter = 10,
                            epsilon = 0.001){

  library(CVXR)
  if(missing(alpha)){
    stop("The value of alpha as in shrinkage intensity not provided, please specify alpha")
  }

  ##################  Building matrix of common samples for pairwise comparisons  ####################

  binary_indicator = matrix(1, nrow(data_with_missing), ncol(data_with_missing))
  binary_indicator[is.na(data_with_missing)]= 0
  common_samples = t(binary_indicator)%*%binary_indicator
  diag(common_samples) = 0


  ###############  compute pairwise covariance/correlation matrix   #######################

  pairwise_cov = cov(data_with_missing, use = "pairwise.complete.obs")
  sigma_vals = sqrt(diag(pairwise_cov))
  pairwise_cor = cov2cor(pairwise_cov)
  pairwise_cor[is.na(pairwise_cor)] = 0
  pairwise_cor[pairwise_cor > 0.95] = 0.95
  pairwise_cor[pairwise_cor < -0.95] = -0.95
  diag(pairwise_cor) = 1
  common_samples[common_samples <= 2] = 2
  pairwise_cov = diag(sigma_vals) %*% pairwise_cor %*% diag(sigma_vals)

  ###############  Compute pairwise Fisher Z-scores   ##########################

  pairwise_zscores = apply(pairwise_cor, c(1,2), function(x) return (0.5*log((1+x)/(1-x))))
  diag(pairwise_zscores) = 0

  ################  Bound on the covariances   ##########################

  bound1 = 12*exp(2*pairwise_zscores)/((exp(2*pairwise_zscores) + 1)^2)
  zscores_sd_1 = sqrt(1/(common_samples - 1) + 2/(common_samples - 1)^2)
  overall_bound_1 = bound1*zscores_sd_1 + zscores_sd_1^2*2*sqrt(3)

  common_samples_2 = matrix(dim(data_with_missing)[1], dim(common_samples)[1], dim(common_samples)[2])
  zscores_sd_2 = sqrt(1/(common_samples_2 - 1) + 2/(common_samples_2 - 1)^2)
  overall_bound_2 = bound1*zscores_sd_2 + zscores_sd_2^2*2*sqrt(3)

  delta = apply(abs(overall_bound_1) + abs(overall_bound_2), c(1,2), function(x) return(pmin(2,x)))
  diag(delta) = 0
  delta_cov = diag(sigma_vals) %*% delta %*% diag(sigma_vals)


  #################################  Use adaptive regularized GLASSO  ############################

  Weight = matrix(1, nrow(delta_cov), ncol(delta_cov))
  Omega_hat = diag(nrow(delta_cov))
  for(iter in 1:max_iter){
    Omega_hat_old = Omega_hat
    Omega <- Semidef(dim(common_samples)[1])
    scale <- Weight*abs(alpha) + lambda*delta_cov
    obj = Minimize(-log_det(Omega) + matrix_trace(Omega %*% pairwise_cov) + sum(mul_elemwise(scale, abs(Omega))))
    prob <- Problem(obj)
    result <- solve(prob)
    R_hat <- base::solve(result$getValue(Omega))
    Omega_hat <- result$getValue(Omega)
    rel_error = sqrt(sum((Omega_hat - Omega_hat_old)^2))/sqrt(sum(Omega_hat^2))
    cat("The relative error in estimated Inverse correlation matrix between last two runs is", rel_error, "\n")
    Weight = 1/((abs(Omega_hat))^{expo} + shift)
    if(rel_error < 1e-03){
      break
    }
  }
  cat("Finished iterations!")
  PR_hat = -cov2cor(as.matrix(Omega_hat))
  diag(PR_hat) = 1
  return(PR_hat)
}