To install the last version of this package directly from GitHub uncomment and run:

# library(devtools)
# use "quiet = FALSE" if you want to see the outputs of this command
# devtools::install_github("juancolonna/FastStepGraph", quiet = TRUE, force = TRUE)

# Then, load it:
library(FastStepGraph)

# If you directly cloned the github repository, 
# then you should uncomment these lines to load the functions:
# source('FastStepGraph.R')
# source('SigmaAR.R')

Simulate Gaussian Data with an Autoregressive (AR) Model:

set.seed(1234567)
phi <- 0.4 
p <- 50  # number of variables (dimension)
n <- 30 # number of samples

# Generate Data from a Gaussian distribution 
data <- FastStepGraph::SigmaAR(n, p, phi)

Afterwards, fit the Omega matrix by calling the Fast Step Graph function, like:

t0 <- Sys.time() # INITIAL TIME
G <- FastStepGraph::FastStepGraph(data$X, alpha_f = 0.22, alpha_b = 0.14)
difftime(Sys.time(), t0, units = "secs")
#> Time difference of 0.07029915 secs
# print(G$Omega)

If the nei.max argument is omitted, it will be 5. If you don’t know the alpha_f and alpha_b values, the use cross-validation. To find the optimal \(\mathbf{\alpha_f}\) and \(\mathbf{\alpha_b}\) parameters for the previously generated X data, we can perform a cross-validation on a combination grid as follows:

t0 <- Sys.time() # INITIAL TIME
res <- FastStepGraph::cv.FastStepGraph(data$X, data_shuffle = FALSE)
difftime(Sys.time(), t0, units = "secs")
#> Time difference of 3.377042 secs

# print(res$alpha_f_opt)
# print(res$alpha_b_opt)
# print(res$Omega)

The arguments n_folds = 5, alpha_f_min = 0.1, alpha_f_max = 0.9, n_alpha = 32 (size of the grid search) and nei.max = 5, have defaults values and can be omitted. Note that, cv.FastStepGraph(X) is not an exhaustive grid search over \(\mathbf{\alpha_f}\) and \(\mathbf{\alpha_b}\). This is a heuristic that always sets \(\mathbf{\alpha_b}\) = \(\frac{\mathbf{\alpha_f}}{2}\). It is recommended to shuffle the rows of X before running cross-validation. The default value is data_shuffle = TRUE, but if you want to disable row shuffle, set it to data_shuffle = FALSE.

To increase time performance, you can run cv.FastStepGraph(X, parallel = TRUE) in parallel. Before, you’ll need to install and register a parallel backend. To run on a Linux system the doParallel dependency must be installed install.packages("doParallel"). These parallel packages will also require the following dependencies: foreach, iterators and parallel. Make sure you satisfy them. Then, call the method setting the parameter parallel = TRUE, as follows:

t0 <- Sys.time() # INITIAL TIME
# use 'n_cores = NULL' to set the maximum number of cores minus one on your machine 
res <- FastStepGraph::cv.FastStepGraph(data$X, parallel = TRUE, n_cores = 2)
difftime(Sys.time(), t0, units = "secs")

# print(res$alpha_f_opt)
# print(res$alpha_b_opt)
# print(res$Omega)

Remember, you can set the n_cores parameter to a value equal to the number of cores you have, but be careful as this may freeze your system. Setting it to 1 disables parallel processing, and setting it to a number greater than the number of available cores does not improve efficiency.

  1. Institute of Computing. Federal University of Amazonas. Brasil. ↩︎

  2. Mathematics Department. National University of Río Cuarto. Argentina. ↩︎