simulation_study/p15_n90/simulation_study_p15_n90_JGL_mgm.R

In JacobHelwig/covdepGE: Covariate Dependent Graph Estimation

rm(list = ls())
library(covdepGE)
library(foreach)
library(JGL)
library(mclust)
library(mgm)

(now <- format(Sys.time(), "%Y%m%d_%H%M%S"))

# initialize storage for results, time, and progress tracking
set.seed(1)
n_trials <- 100
results <- vector("list", n_trials)
names(results) <- c(paste0("trial", 1:n_trials))
pb <- txtProgressBar(0, n_trials, style = 3)

# define data dimensions
p <- 15
(n <- 2 * 3 * p)
(nj <- n %/% 3)

# p <- 5
# n <- 180
# (nj <- n %/% 3)

# generate the data
data_list <- replicate(n_trials, generateData(p, nj, nj, nj), F)

# get number of available workers and register parallel backend
(num_workers <- min(10, parallel::detectCores() - 5))
doParallel::registerDoParallel(num_workers)

eval_est <- function(est, true){

  # get n
  n <- dim(est)[3]

  # get true number of edges and non-edges
  num_edge <- sum(true, na.rm = T)
  num_non <- sum(true == 0, na.rm = T)

  # calculate sensitivity, specificity, etc.
  true_edge <- sum(est == 1 & true == 1, na.rm = T)
  false_edge <- sum(est == 1 & true == 0, na.rm = T)
  true_non <- sum(est == 0 & true == 0, na.rm = T)
  false_non <- sum(est == 0 & true == 1, na.rm = T)
  sens <- true_edge / num_edge
  spec <- true_non / num_non

  list(sens = sens, spec = spec, TP_n = true_edge / n, FP_n = false_edge / n,
       TN_n = true_non / n, FN_n = false_non / n)
}

# function to turn an array into a list of sparse matrices
sp.array <- function(arr, n){
  lapply(1:n, function(l) Matrix::Matrix(arr[ , , l], sparse = T))
}

# function to approximate the AIC for JGL
aic_JGL <- function(X, prec){

  # iterate over each of the clusters
  aic <- 0
  for (k in 1:length(X)){

    # fix the data for k-th cluster; get n and covariance
    n_k <- nrow(X[[k]])
    cov_k <- cov(X[[k]])

    # 3 terms in AIC
    aic1 <- n_k * sum(diag(cov_k %*% prec[[k]]))
    aic2 <- -n_k * log(det(prec[[k]]))
    aic3 <- 2 * sum(prec[[k]] != 0)
    aic <- aic + aic1 + aic2 + aic3
  }

  # verify that the aic is valid and return
  aic <- ifelse(is.numeric(aic), aic, Inf)
  aic
}

# function to perform clustering, cross-validation and evaluation for JGL
JGL.eval <- function(X, Z, true){

  start0 <- Sys.time()

  # cluster the data based on Z
  clust <- Mclust(Z, verbose = F)
  X_k <- lapply(1:clust$G, function(k) X[clust$classification == k, ])

  # create a grid of lambda1 and lambda2
  lambda1_min <- 0.15
  lambda2_min <- 1e-5
  lambda1_max <- 0.4
  lambda2_max <- 0.01
  lambda1 <- seq(lambda1_min, lambda1_max, 0.005)
  lambda2 <- exp(seq(log(lambda2_min), log(lambda2_max),
                     length = length(lambda1) %/% 2))

  # optimize lambda1 with lambda2 fixed as the smallest value
  aic_lambda1 <- vector("list", length(lambda1))
  for(k in 1:length(lambda1)){

    # fit the model and return lambda, AIC, and time to fit
    start <- Sys.time()
    out <- JGL(Y = X_k,
               lambda1 = lambda1[k],
               lambda2 = lambda2_min,
               return.whole.theta = T)
    time <- as.numeric(Sys.time() - start, units = "secs")
    aic_lambda1[[k]] <- list(lambda = lambda1[k], aic = aic_JGL(X_k, out$theta),
                             time = time)
  }

  # fix lambda 1 and optimize lambda2
  lambda1_opt <- sapply(aic_lambda1, `[[`, "aic")
  lambda1_opt <- lambda1[which.min(lambda1_opt)]
  aic_lambda2 <- vector("list", length(lambda2))
  for(k in 1:length(lambda2)){

    # fit the model and return lambda, AIC, and time to fit
    start <- Sys.time()
    out <- JGL(Y = X_k,
               lambda1 = lambda1_opt,
               lambda2 = lambda2[k],
               return.whole.theta = T)
    time <- as.numeric(Sys.time() - start, units = "secs")
    aic_lambda2[[k]] <- list(lambda = lambda2[k], aic = aic_JGL(X_k, out$theta),
                             time = time)
  }

  # select the optimal lambda2 and fit the final model
  lambda2_opt <- sapply(aic_lambda2, `[[`, "aic")
  lambda2_opt <- lambda2[which.min(lambda2_opt)]
  out <- JGL(Y = X_k,
             lambda1 = lambda1_opt,
             lambda2 = lambda2_opt,
             return.whole.theta = T)

  # record time
  out$time <- as.numeric(Sys.time() - start0, units = "secs")

  # save the lambda grid, optimal lambda and classification
  out$lambda1_grid <- aic_lambda1
  out$lambda2_grid <- aic_lambda2
  out$lambda1 <- lambda1_opt
  out$lambda2 <- lambda2_opt
  out$classification <- clust$classification

  # get the estimated graphs
  n <- nrow(X)
  p <- ncol(X)
  out$str <- array(unlist(out$theta[clust$classification]), c(p, p, n))
  out$str <- (out$str != 0) * 1 - replicate(n, diag(p))

  # get performance, convert graphs to a sparse array, and return
  perf <- eval_est(out$str, true)
  out[names(perf)] <- perf
  out$str <- sp.array(out$str, n)
  out
}

# function to perform bandwidth selection, run tvmgm, and evaluate the results
tvmgm.eval <- function(X, Z, true){

  start <- Sys.time()

  # re-scale Z to [0, 1]
  z01 <- Z - min(Z)
  z01 <- z01 / max(z01)

  # choose optimal bandwidth
  p <- ncol(X)
  bw <- bwSelect(data = X,
                 type = rep("g", p),
                 level = rep(1, p),
                 bwSeq = seq(0.1, 0.4, 0.1),
                 bwFolds = 5,
                 bwFoldsize = 5,
                 modeltype = "mgm",
                 k = 2,
                 pbar = F,
                 timepoints = z01)
  bw <- as.numeric(names(which.min(bw$meanError)))

  # run tvmgm
  out <- tvmgm(data = X,
               type = rep("g", p),
               level = rep(1, p),
               timepoints = z01,
               estpoints = z01,
               bandwidth = bw,
               k = 2,
               pbar = F)

  # record the time
  out$time <- as.numeric(Sys.time() - start, units = "secs")

  # save the selected bandwidth and remove large objects
  out$bw <- bw
  out$tvmodels <- out$interactions <- out$intercepts <- NULL

  # get graphs, remove pairwise (it is large)
  out$str <- (out$pairwise$wadj != 0) * 1
  out$pairwise <- NULL

  # get performance, convert graphs to a sparse array, and return
  perf <- eval_est(out$str, true)
  out[names(perf)] <- perf
  out$str <- sp.array(out$str, n)
  out
}

functions <- c("aic_JGL", "eval_est", "JGL.eval", "sp.array", "tvmgm.eval")
packages <- c("JGL", "mclust", "mgm")

# perform trials
results <- foreach(j = 1:n_trials, .export = functions,
                   .packages = packages)%dopar%
  {
    # record the time the trial started
    trial_start <- Sys.time()

    # get the data and create storage for the models (j=1)
    data <- data_list[[j]]
    trial <- vector("list", 2)
    names(trial) <- c("mgm", "JGL")

    # convert the true precision to an array and then to a graph; mask diagonal
    prec <- array(unlist(data$true_precision), c(p, p, n))
    graph <- (prec != 0) * 1 + replicate(n, diag(rep(NA, p)) * 1)

    # fit each method

    # mgm
    out_mgm <- tryCatch(tvmgm.eval(X = data$X,
                                   Z = data$Z,
                                   true = graph),
                        error = function(e) list(error = e))
    if (!is.null(out_mgm$error)){
      message("mgm ERROR:", out_mgm$error)
      next
    }
    trial$mgm <- out_mgm
    rm(list = "out_mgm")
    gc()

    # JGL
    out_JGL <- tryCatch(JGL.eval(X = data$X,
                                 Z = data$Z,
                                 true = graph),
                        error = function(e) list(error = e))
    if (!is.null(out_JGL$error)){
      message("JGL ERROR:", out_JGL$error)
      next
    }
    trial$JGL <- out_JGL
    rm(list = "out_JGL")
    gc()

    # return the trial
    message("\nTrial ", j, " complete ", Sys.time(), "\n")
    trial
  }

# save the results and stop the cluster
save(results, file = paste0("res_p", p, "_n", n, "_JGL_mgm_", now, ".Rda"))
doParallel::stopImplicitCluster()