library(covdepGE)
library(loggle)
library(JGL)
library(mclust)
library(mgm)
# function to fit and evaluate results for covdepGE
covdepGE.eval <- function(X, Z, hp_method, true, n_workers, max_iter_grid){
start <- Sys.time()
# get dimensions of the data and fit covdepGE
n <- nrow(X)
p <- ncol(X)
out <- covdepGE(X = X,
Z = Z,
hp_method = hp_method,
parallel = n_workers > 1,
num_workers = n_workers,
max_iter_grid = max_iter_grid,
prog_bar=FALSE)
# record time and get the array of graphs
out$time <- as.numeric(Sys.time() - start, units = "secs")
out$str <- array(unlist(out$graphs$graphs), dim = c(p, p, n))
# covert the unique graphs to a list of sparse matrices
out$unique_graphs <- out$graphs$unique_graphs
for (k in 1:length(out$unique_graphs)){
out$unique_graphs[[k]]$graph <- Matrix::Matrix(
out$unique_graphs[[k]]$graph, sparse = T)
}
# remove large objects, put the unique graphs back in the graphs sublist
out$pip <- out$graphs$inclusion_probs_sym
out$variational_params <- out$graphs <- out$weights <- NULL
out$graphs$unique_graphs <- out$unique_graphs
out$unique_graphs <- 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$str, n)
message("\ncovdepGE complete ", Sys.time(), "\n")
out
}
# function to approximate the AIC for JGL
aic_JGL <- function(X, prec){
# iterate over each of the clusters
aic <- 0
for (k in 1:length(X)){
# fix the data for k-th cluster; get n and covariance
n_k <- nrow(X[[k]])
cov_k <- cov(X[[k]])
# 3 terms in AIC
aic1 <- n_k * sum(diag(cov_k %*% prec[[k]]))
aic2 <- -n_k * log(det(prec[[k]]))
aic3 <- 2 * sum(prec[[k]] != 0)
aic <- aic + aic1 + aic2 + aic3
}
# verify that the aic is valid and return
aic <- ifelse(is.numeric(aic), aic, Inf)
aic
}
# function to perform clustering, cross-validation and evaluation for JGL
JGL.eval <- function(X, Z, true){
start0 <- Sys.time()
# cluster the data based on Z
clust <- Mclust(Z, verbose = F, G = 2:12)
X_k <- lapply(1:clust$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()
# if the covariate is multidimensional, sort observations in X and ground truth
if (ncol(Z) > 1){
sort_inds <- sort_Z(Z)
X <- X[sort_inds, ]
true <- true[sort_inds]
Z <- 1:nrow(X)
}
# get dimensions of the data
n <- nrow(X)
p <- ncol(X)
# re-scale Z to [0, 1]
z01 <- Z - min(Z)
z01_est <- z01 <- z01 / max(z01)
# choose optimal bandwidth
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$meanError)))
# run tvmgm
out <- tvmgm(data = X,
type = rep("g", p),
level = rep(1, p),
timepoints = z01,
estpoints = z01_est,
bandwidth = bw,
k = 2,
pbar = F)
# record the time
out$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$str, n)
out
}
# function to fit and evaluate results for loggle
loggle.eval <- function(X, Z, true, n_workers, cutoff){
start <- Sys.time()
# if the covariate is multidimensional, sort observations in X and ground truth
if (ncol(Z) > 1){
sort_inds <- sort_Z(Z)
X <- X[sort_inds, ]
true <- true[sort_inds]
}
# get dimensions of the data
n <- nrow(X)
p <- ncol(X)
# determine if the covariate is discrete
Z_star <- unique(Z)
discrete <- length(Z_star) <= 2
# there are issues with estimating graphs at the end points of the time
# interval; don't estimate these
pos <- (cutoff + 1):(n - cutoff)
# pos <- cutoff:(n - cutoff)
# fit loggle
# out <- R.utils::withTimeout(
# quiet(loggle.cv(t(X),
# pos = pos,
# d.list = c(0, 0.001, 0.01, 0.025, 0.05, 0.075, 0.1, 0.15, 0.2),
# num.thread = n_workers)),
# timeout = 2 * 60 * 60 * n_workers)
out <- quiet(loggle.cv(t(X),
pos = pos,
d.list = c(0, 0.001, 0.01, 0.025, 0.05, 0.075, 0.1, 0.15, 0.2),
num.thread = n_workers))
closeAllConnections()
# record time and get the array of graphs
out$time <- as.numeric(Sys.time() - start, units = "secs")
out$str <- array(NA, dim = c(p, p, n))
for (j in 1:n){
# if the observation is in the cutoff region, assign the graph for the last
# observation outside of the cutoff region
if (j %in% pos){
graph_j <- out$cv.select.result$adj.mat.opt[[j - cutoff]]
# print(paste('in', j, j-cutoff))
}else if (j < cutoff + 1){
# print(j)
graph_j <- out$cv.select.result$adj.mat.opt[[1]]
}else if (j > n - cutoff){
# print(paste(j, n - 2 * cutoff, length(pos)))
graph_j <- out$cv.select.result$adj.mat.opt[[n - 2 * cutoff]]
}else{
stop(paste0('Error in resolving cutoff regions for j=', j))
}
out$str[,, j] <- as.matrix(graph_j - diag(p))
}
# remove large objects
out$cv.result.h <- NULL
# get performance, convert graphs to a sparse array, and return
perf <- eval_est(out$str, true)
out[names(perf)] <- perf
out$str <- sp.array(out$str, n)
message("\nloggle complete ", Sys.time(), "\n")
out
}
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