This repository contains the code developed in the context of the paper Cibinel et al. (2024), which includes both the implementation of the Generalised Iterative Conditional Fitting (see below), the simulation studies and the practical analyses that have been conducted.
The algorithm is provided both in the form of the R package
gicf and as the original R/C++ scripts created during the
development of the methodology. The structure of the repository mirrors
that of the R package submitted to CRAN, with all the information needed
for the reproducibility of the results presented in Cibinel et
al. (2024) stored in the folder
Simulations and analysis.
To install from CRAN (recommended):
install.packages("gicf")
library(gicf)To install directly from this repository:
library(devtools)
install_github("luca-cibinel/gicf", build_vignette = F)
library(gicf)The Generalised Iterative Conditional Fitting optimises the penalised Gaussian loglikelihood
\[-\log{|\Sigma|} - \text{tr}(\Sigma^{-1}S) - \lambda\|\Sigma - \text{diag}(\Sigma)\|_1 - \kappa\|\text{diag}(\Sigma^{-1})\|_1,\]
under the constraint that \(\Sigma\) satisfies a given pattern of zeros.
The package also implements some helper functions which allow to compute the maximum value of the parameters \(\kappa\) and \(\lambda\) for which the solution is not trivial.
Inside the folder Simulations and analysis there are the
files used to perform both the simulation studies and the analysis on
the sonar data. These use a local implementation of the GICF algorithm
(equivalent to the gicf package), contained in the folder
Simulations and analysis/gicf. When executing the R
scripts, the working directory should be set to the directory of the
script.
The folder Simulations and analysis/simulations contains
the simulated data and the R scripts of the simulation studies: -
simulation_mle.R compares the MLE estimate versus the
ridge-regularised estimate of \(\Sigma\) in under the specification of an
adjacency matrix. - simulation_time.R compares the
computational time required to the GICF and the covglasso algorithms to
estimate a sparse covariance matrix under a known sparsity pattern. -
simulation_lasso.R compares the covglasso estimate versus
the ridge-regularised covglasso estimate of \(\Sigma\).
The data contained in the
Simulations and analysis/simulations/data are simulated
datasets sampled from a multivariate normal distribution with mean \(0\). Each dataset is described by two
files:
sigma_mod_RB_d_[D]_p_[P]_n_[N].dat
simul_mod_RB_d_[D]_p_[P]_n_[N].datwhere the prefix sigma indicates the file which contains
the true covariance matrix and the prefix simul contains
the simulated data. In the name of each file, D indicates
\(10\) times the density of the
covariance matrix, P indicates the number of covariates and
N indicates the number of observations. The simulations
regarding computational time are an exception to this format, due to the
large amount of data used in this study. Instead of relying on a local
copy of the data, new data are sampled each time, using the true
covariance matrix stored in the appropriate .dat file. The
original datasets can be made available upon request.
The folder
Simulations and analysis/simulations/environments contains
one R environment for each simulation study. If these environment are
loaded, the output can be recovered by running the section “OUTPUT”.
Inside the folder
Simulations and analysis/sonar data analysis there is the R
script which performs the analysis. The data is downloaded directly by
the script.
Together with the script there are two R environments, for the banded and non-banded estimators, which contain the computed values of the cross validation objective function, used to perform model selection. If those enviornments are loaded, the output can be recoverd directly by running the section “OUTPUT”.