Graphical Independence Filtering


One of the fundamental problems in data mining and statistical analysis is to detect the relationships among a set of variables. To this end, researchers apply undirected graphical models in work, which combine graph theory and probability theory to create networks that model complex probabilistic relationships. By estimating the underlying graphical model, one can capture the direct dependence between variables. In the last few decades, undirected graphical models have attracted numerous attention in various areas such as genetics, neuroscience, finance and social science.

When the data is multivariate Gaussian distributed, detecting the graphical model is equivalent to estimating the inverse covariance matrix. gif package provides efficient solutions for this problem. The core functions in gif package are hgt and sgt.

These functions based on graphical independence filtering have several advantages:

Method (p = 1000) (p = 4000) (p = 10000)
hgt 0.395s 6.668s 46.993s
sgt 0.225s 3.099s 21.454s
QUIC 1.580s 117.041s 1945.648s
fastclime 62.704s *** ***

Particularly, hgt provides a solution for best subset selection problem in Gaussian graphical models and sgt offers closed-form solution equivalent to graphical lasso when the graph structure is acyclic.


CRAN Version

To install the gif R package from CRAN, just run:


Github Version

To install the development version from Github, run:

install_github("Mamba413/gif/R-package", build_vignettes = TRUE)

Windows user will need to install Rtools first.


Take a synthetic dataset as a simple example to illustrate how to use hgt and sgt to estimate the underlying graphical model.

Simulated Data

We extract 200 samples from the graphical model with (p = 100) and whose graph structure is the so-called AR(1). A sketch of the example could be seen in the following picture.


Users estimate the underlying (K)-sparse graph model via Hard Graphical Thresholding algorithm when a specific model size (K) is given. The hgt function would return a (p p) matrix with number of non-zero off-diagonal entries in the upper-triangular part equal to (K) and a (K 2) matrix marks down the corresponding active entries.

res <- hgt(ar1[["x"]], size = 99)


For Soft Graphpical Thresholding algorithm, users could estimate the underlying model with given regularization parameter (). In the return, we not only provide the parameter matrix and the corresponding active entries mentioned above, but also a boolean flag indicating whether the estimated graph structure is acyclic, since the solution would be equivalent to graphical lasso if the graph is acyclic.

res <- sgt(ar1[["x"]], lambda = 0.01)


GPL (>= 2)